UNIVERSITY OF P ISA

Department of Jurisprudence

Master's Degree in Law

Thesis

THE THEORY OF DESIGN OF MECHANISMS: ORIGINS AND APPLICATIONS

Applicant: Rapporteur :

Lorenzo Lari Chiar.mo Prof. Nicola Giocoli

ANNO ACCADEMICO 2012/2013

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INDEX :

INTRODUCTION .................................... ..6

CHAP.1: THE THEORY OF THE DRAWING OF THE

MECHANISMS ........................ ................... 10

1.1 ADAM SMITH AND THE INVISIBLE HAND ... ...... ..10

1.2 THE DEBATE ON CENTRALIZED PLANNING ....................................... ..... 13

1.3 FROM PARETO TO BARON TO VON MISES ...... ..16

1.4 FRIEDRICH AUGUST VON HAYEK ............ ... 20

1.5 I NOBEL 2007: HURWICZ, MYERSON AND MASKIN ...................................................... ... 23

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CHAP.2: THE CONTRIBUTION OF LEONID

Hurwicz ................................. ...... 28

2.1 BIOGRAPHICAL NOTES ................................. ... 28

2.2 MATHEMATICS AT THE SERVICE OF THE ECONOMY .......................................... ......... 33

2.3 THEORETICAL CONTRIBUTION ........................ .34

2.4 WHAT IS A MECHANISM ........................... 37

2.5 THE HURWICZ TECHNICAL CONQUESTS ...................................................... 41

2.6 DEVELOPMENTS OF THEORY ........................ ... 43

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CHAP.3: ROGER MYERSON AND ERIC

MASKIN ............................................. ... 48

3.1 ROGER B. MYERSON .............................. ... 48

3.2 THE BIRTH OF INTEREST FOR THE THEORY OF GAMES ........................................ 49

3.3 FIRST WORKS .......................................... .51

3.4 REVELATION PRINCIPLE ..................... ..55

3.5 RECOGNITIONS FOR THE THEORY OF GAMES ......................................................... 58

3.6 ERIC S. MASKIN ....................................... .62

3.7 THEORY OF IMPLEMENTATION ......... ..... 63

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3.8 MASKIN MONONICITY AND THE YEARS OF HARVARD ...................... ........................... ..... 67

CHAP.4: APPLICATIONS .................. ... ... ..... 70

4.1 INTRODUCTION .................................... ..... 71

4.2 THE CASE OF PUBLIC GOODS .................. ..... 72

4.3 ELECTIONS AND FINANCE .............................. ... 74

4.4 ECONOMIC REGULATION ............... .......... 76

4.5 TYPES OF REGULATION .. .................. .81

4.6 INCENTIVE REGULATION ........................ ... 83

4.7 RESOLVING THE HAYEK INFORMATION PROBLEM ......... .. ............................................. ..86

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4.8 A MECHANISM OF AUCTION FOR UMTS FREQUENCIES ............ ... ........................ ..92

4.9 BANK REGULATION ......... ..... 95

CONCLUSIONS .................................... .100

REFERENCES .................................... 107

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INTRODUCTION

What do Mario Balotelli, Sergio Marchionne, Trenitalia and Umts have in common, then in the order a top player, a top manager, a natural monopolist and a recent telecommunications protocol?
At first glance it may seem that these elements are not connected, but in reality there is an economic theory that manages to connect them all. This theory is called the design theory of mechanisms and explains how we should remunerate and adjust the salary and bonuses of a footballer or manager, incentivizing them to make him
achieve more efficient results, whether they are indistinctly goals, assists or profits; or how to regulate a natural monopoly like the Italian railways in order to have an efficient balance between the price for travelers and the profit for the monopolistic company, or how to design a public auction mechanism that
allows the State to assign the spectrum of the umts frequencies with the greatest possible economic return.
In the simplest way possible, the design theory of the mechanisms analyzes how institutions, contracts, auctions and social organizations are structured so that they produce the desired effects. The theory is extremely general and has infinite possibilities of application.
The theory of mechanism design (MDT) has obtained the highest recognition academic October 15, 2007 when the Sveriges Riksbank (Sweden's central bank) has awarded the Prize in
Economic Sciences in Memory of Alfred Nobel to the three scholars
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have contributed most to it, Leonid Hurwicz, Roger
Bruce Myerson and Eric Maskin.
The founding father of the theory was Hurwicz, whose initial interest was in the theory of general economic equilibrium, to which he made various contributions. But the model of general equilibrium formulated and refined in the 50s and 60s was, and is, a model in which the problems deriving from the presence of private information are not considered and therefore a fundamental role of the price system, transmit information on the 'abundance or scarcity of a given resource, it is difficult to analyze.
Hurwicz's fundamental intuition was to formulate the problem of allocating economic resources as a problem of transmitting information. Until then, these problems had been analyzed in 'team theory', but the point of view was more engineering than economic. That is, we wondered how a group of people with shared objectives could transmit effectively (avoiding communication errors, for example) the information necessary to achieve the common good. Hurwicz inserted the distinctly economic dimension of the problem: in many relevant cases we can not absolutely assume that social goals are shared, and we must accept the fact that economic agents will try to use their private information to their advantage. The attention, from that
moment on, it is therefore postponed by engineering problems
(minimizing communication errors) to more problems
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strictly economic (provide agents the incentive to tell the truth).
Hurwicz's work laid the groundwork for a much deeper understanding of economic institutions, be they markets, businesses or public bodies. Finally it became possible to formally analyze the enormous incentive problems that characterized the planned socialist economies. Finally it became possible to seriously discuss the organization of the markets.
Maskin and Myerson developed these themes. Starting from the second half of the '70s, in a research work that continues to this day, they have shown the implications of the existence of private information for the design of economic and social organizations. Both have made very important contributions not only to the economy, but also to political science and applied mathematics. Both have made fundamental contributions to auction theory; In particular, Myerson was the first to provide analytical tools for the analysis of optimal sales mechanisms.
In the first chapter I will talk about the origins of the theory; It was born as a brilliant answer to the debate on centralized planning of the thirties.
In the second chapter I will focus on the figure of Leonid Hurwicz and his great contribution to the MDT theory, not only from the analytical point of view but also through the historical and personal events that
led him to become the father of the theory.
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In the third chapter I will analyze the other two great contributions of Myerson and Maskin to the theory, again not only from the analytical point of view, but also through the events that allowed these two scholars to continue and refine the work begun by Hurwicz.
In the fourth chapter I will list some of the infinite applications of the theory, whose level of activity is increasingly relevant and current; in particular I will focus on elections, finance, banking regulation, public goods, natural monopolies, the
regulation in general, and auctions.
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CHAPTER 1

THE THEORY OF THE DESIGN OF MECHANISMS

The economic resources in the history of mankind have always been limited and economists have always posed the problem of being able to guarantee the greatest possible social well-being. Mechanism design theory starts from this classic economic problem of resource allocation and not only solves it
but goes even further.
The history of economic literature is full of theories that attempt to solve the problem and it is important to analyze this background to understand where the mechanism design theory fits.

1.1 ADAM SMITH AND THE INVISIBLE HAND

Our excursus begins with the father of liberalism, Adam Smith 1 , witness of the transformations that affect the economic life of England, in which the mechanisms of modern industrial capitalism are being affirmed, albeit in an embryonic form.
Smith does not deny that the driving force of every economic activity is individual interest. But when considering the
individual interests and socio-economic processes that they give rise to

1 A. Smith (1776).

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general rather than particular, we see that they find their harmonization in the whole and therefore lead to a
general advantage from which even those who are apparently disadvantaged profit.
There is therefore an invisible hand that guides the individual interests beyond their specific intentions, composing them in a totality that escapes the partial gaze of the individual.
Smith therefore shares the optimistic assumptions of enlightenment in general and of French physiocracy. For this reason, he considers, once again taking up a suggestion from the Parisian physiocrats, that the action of the State in terms of economics, regulating production processes and introducing restrictions on the freedom of trade, is completely harmful. In fact, it risks compromising that general advantage that is necessarily acquired when things are allowed to follow their ordinary natural course.
As an alternative to the economic policy of the seventeenth-century mercantilism, which provided for massive interventions by the state, especially in the defense of national production with customs or bans on the importation of foreign goods, Smith and the French physiocrats advocate the establishment of the most complete economic liberalism. The only legitimate intervention by the state is to levy taxes on individuals' private gains so as to guarantee those public services that then benefit everyone and everyone. With Smith, political economy, that is, the art of well-administering the economic life of the State, thus emerges from the sphere of
empirical precepts to aspire to the status of a real science.
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Let us now take a more in-depth look at the question of the invisible hand: for Smith the intervention of the state in the economy is not necessary and each one must make his own interests; if everyone makes their own interests it is obvious that the collective wealth will increase to some extent and everyone will enjoy the benefits, albeit in different ways: those who invest earn more than the poor, but the latter will also have a positive increase in wealth.
As Smith states "looking for how much he can use his capital to support the domestic industry and to direct this industry so that his product can have maximum value, each individual necessarily contributes as much as he can to maximizing the company's annual income. He only seeks his own profit, and in this, as in many other cases, he is led by an invisible hand to promote an end that was not his intentions: By pursuing his own interests, he often promotes that of society more effectively than when
it really intends to promote it ". (SMITH A. (1971), "Sketch of the
Wealth of Nations," p.584 ).
What can be considered a vice in the private field, that is to do one's own interests, becomes a virtue in the public sphere.
Smith's theory is one of the cornerstones of liberal thought and justifies positions in favor of free trade and the opening of markets.
By defining a market economy an economic system in which resources are allocated by means of the decentralized decisions of
agents guided by their own self-interest, the invisible hand guarantees us
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that such an economy is capable of spontaneously determining the efficient allocation of resources and then produce maximum social well-being. What drives the allocation of resources is their relative scarcity, ie the opportunity cost of their different jobs.
The market mechanism, represented in practice by the relative price system, is the means by which information on scarcity and opportunity costs spread among economic agents. Each agent, guided by price information signals, acts in such a way as to maximize his own interest, but in so doing he unknowingly contributes to determining the outcome of an excellent Pareto 2 on a social level.

1.2 THE DEBATE ON CENTRALIZED PLANNING

The principle of the invisible hand was only rigorously demonstrated in the mid-fifties of the twentieth century 3 , and ensures that under a stringent stringent hypothesis (perfectly competitive and balanced markets), the market works, that is, it really achieves the maximum collective well-being.
We know that the lack of one or more of the hypotheses required for the validity of the principle gives rise to the so-called market failures.
But it is equally interesting to note that the principle does not state that
only the free market mechanism can achieve

2 Principle for which the condition of a subject can not be improved without worsening the condition of another.

3 K. Arrow and G. Debreu (1954).

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the efficient allocation of resources. It identifies the sufficient condition for such allocation in market exchanges guided by price signals, but it does not tell us that it is necessary.
Therefore, starting from the 1930s it seemed natural to many economists with different approaches to propose a different mechanism for allocating resources, centralized planning, and to state that not only through the free market but also through this mechanism it was possible to obtain an allocation efficient 4 .
The debate on the economic calculation, for the scientific stature of the personalities involved, for the theoretical level and the influences that it has had in the subsequent development of our science, is one of the most important and full of consequences in the history of economic thought. Two important contributions on the socialist economic calculation that we must mention are those of Vilfredo Pareto and Enrico Barone.
On the one hand, Pareto's influence concentrated on the mathematical analysis of economic equilibrium, where it is always assumed as a starting point that all the information necessary to develop it is available, thus opening the way to the idea, developed later by Baron and repeated, as we shall see, until satiety by many other economists, that the problem of economic calculation in economies
socialist could be solved mathematically. The point was then

4 N. Giocoli (2009).

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taken up and set by the mathematical economists of equilibrium in the case of a market economy.
Nevertheless, it is necessary to point out that neither Pareto nor Baron are completely guilty of the interpretation we have just analyzed, since both explicitly showed the impossibility of giving a solution to the corresponding system of equations without having the information determined by the market itself. In fact, in 1897 Pareto even went so far as to affirm that the solution to the system of equations describing equilibrium in practice was well beyond the capacity of algebraic analysis, in that case a change of roles was necessary, since mathematics did not he could have continued to help political economy, on the contrary, political economy should have come to the aid of mathematics.
In other words, even if all equations were known in reality, the only valid procedure for resolving them would be to observe the real solution that the market would have already given 5 .
Will then be Arrow and Debreu with their model 6 to show that
if the hypotheses formulated about the conditions in which a market operates are satisfied (ie convexity of preferences, perfect competition and independence of demand), then there will be a series of prices such that the aggregate supply will be equal to the
aggregate demand for each asset in the economy. So there will be a

5 V.Pareto (1906).

6 K. Arrow and G. Debreu (1954).

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general equilibrium to which the market can arrive by itself, but Arrow and Debreu are limited to the result of existence and do not calculate this equilibrium (the vector of prices).
Pareto explicitly denies the possibility that we can dispose of all the necessary information, not even to enunciate the system of equations that would allow us to describe the equilibrium and, at the same time, proposes a subsidiary problem, that of the algebraic impossibility of solving in practice the equation system that describes it formally.
In agreement with Pareto, Enrico Barone highlights in the well-known article of
1908 regarding the application to the collectivist state of the paradigm enunciated for the first time by Pareto 7that, although the practical difficulty of solving algebraically the aforementioned system of equations (which does not constitute a theoretical impossibility) could be overcome, in any case it would be inconceivable (and, therefore, now yes, theoretically impossible) to obtain the whole information necessary to determine the technical coefficients that the formulation of the corresponding system of equations requires.

1.3 FROM PARETO TO BARON TO VON MISES

Pareto and Barone's contributions are ambivalent. In fact, both authors, as we have seen, make explicit reference to the difficulty not only practical to solve the corresponding system of equations; they have had the merit of highlighting also

7 E. Barone (1908).

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the irreconcilable theoretical impossibility of obtaining all the information necessary to describe the equilibrium, a problem presented to every governing body that seeks to obtain the practical information necessary to plan and co-ordinate the company coercively.
The contribution of Ludwig von Mises, whose work is essential to the debate on planning, is focused on this impossibility. Mises states in 1920 that "The distribution of administrative control over economic assets among the individuals of the society participating in production requires a sort of intellectual division of labor that is not possible without a system of calculation and without a market. " 8
The intervention of the Austrian economist in the debate is entirely devoted to the defense of classical liberalism that distinguished the Austrian school 9 and the values ​​that led to the birth of libertarianism. Obviously this implies a hard aversion to socialism that is refuted with solid arguments, highlighting the impossibility of economic calculation.
In reality, it is the prices that guide the rational choices of individuals in a socialist society.
Two years later, in 1922, in his systematic treatise on socialism, Mises goes back to repeating the same idea in an even more
articulate way: "In societies based on the division of labor, the

8 LV Mises (1927), pag.102.

9 Austrian economists distanced themselves profoundly from economists

neoclassical because of the contrast with regard to the economic calculation, a contrast born for the position of important Austrian economists who supported the impossibility of economic calculation in the absence of monetary price and private property.
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distribution of property rights gives rise to a kind of intellectual division or work of mind, without which no type of production or economics would be possible 10 . "
Mises even more than talking about private information leakage, refers to a certain type of intellectual division of labor, which he believes constitutes the essence of the market, and which proportionates and generates the information that makes the calculation or economic evaluation possible that every business decision requires.
And five years later, in 1927, in the work "Liberalismus", Mises explicitly concludes that his analysis is based on the impossibility that socialism can generate practical information in the form of market prices, information necessary to make the division possible. intellectual knowledge that a modern society requires and that arises only as a consequence of the creative capacity of human action or entrepreneurial function:
"The ultimate objection of the economy against socialism is that socialism demands to renounce the intellectual division of labor that is result of the cooperation between all the entrepreneurs, the landowners, and the workers, as producers and consumers, and that it is realized in the definition of the market prices » 11 .
Socialism, therefore, to the extent that it impedes the free exercise of entrepreneurship in the essential area of
production factors (capital goods and natural resources), does not allow

10 LV Mises (1927).

11 LV Mises (1927).

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creation or transmission of the practical information that would be necessary for the central planning body to assign them appropriately. Since this information does not develop, it can not be taken into account in the estimation calculation necessary in any rational economic decision. In this way, the central control body does not even know, when it comes to taking decisions and acting, if it is renouncing to reach certain objectives or ends which, from its point of view, could be of greater importance. The economic decisions in socialism are therefore arbitrary and take place in the most absolute darkness.
At this point, it is very important to underline that Mises's thesis is a theoretical thesis on the intellectual error that any socialist idea implies, since it is not possible to organize the society through compulsory mandates, given the impossibility control is able to obtain the information necessary to do so.
The control body, when issuing an edict or a mandate for or against a given economic project, does not know the information necessary to know whether it has acted correctly or not, so it can not make any calculation or economic evaluation. If it is supposed that the control body has all the necessary information and that no changes occur, it is clear that no problem of economic calculation can arise, since the principle is considered that
this problem does not exist.
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1.4 FRIEDRICH AUGUST VON HAYEK

Mises' work had a strong impact on his young student Friedrich
August von Hayek who, consequently, abandoned the
"well-meaning" socialism of early youth and, since then, devoted a considerable intellectual effort to purify and expand the contributions of his teacher.
Hayek's contribution to the debate of the Thirties basically moves from the objection to the idea that it was possible to explicitly solve the system of equations of general equilibrium.
This is generally interpreted as a practical objection relating to the difficulty in collecting and manipulating the information necessary for this purpose. Hayek, however, stresses that it is not so much the practical difficulty of gathering detailed information, but accessible to all, as the theoretical impossibility of centralizing those knowledge of particular circumstances of time and place, which tacitly dispose of thousands or millions of different individuals.
Despite this radical interpretation, the Hayekian criticism is sufficient to induce socialist planning advocates to adopt a new type of argumentation.
Hayek then notes that the expected decentralization of production decisions does not stop the need to centralize a vastly greater body of knowledge in the planning and control body than it can actually acquire. In fact, if this body intends to exert any control over the managers
of state-owned enterprises (which is all the more necessary because
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automatic control of the
competitive market is excluded ), it must be able to know the cost functions on which the managers operate; but this implies a detailed knowledge of the technical conditions and the particular circumstances in which the individual companies are located.
Even more serious problems arise with regard to decisions concerning the allocation of funds for investments.
Given the inexistence of a capital market, these decisions must be taken by the authority responsible for the plan, but the attempt to set rational criteria for these decisions raises theoretical and practical problems
of difficult solution. 12
Therefore, the essentially erroneous thesis according to which there are two distinct theses against the possibility of economic calculation in socialist economies can not be accepted. The first of these theses
it would simply be algebraic or computational, and would have been initially expressed by Mises, according to whom the economic calculation would not be possible where there are no prices that allow the calculation of gains and losses; and the other of an epistemological nature, developed mainly by Hayek, by virtue of which socialism could not work because it is impossible for the central planning body to have the relevant practical information necessary for organizing society.
On the contrary, for Mises both the thesis, the computational
one and the epistemological one, are nothing but the two inseparable faces

12 FV Hayek (1937).

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of the same coin. On the one hand, it is not possible to make any economic calculation, nor the corresponding assessments, if the necessary information can not be provided to make it concrete in the form of market prices, on the other, this information is constantly arising as a result of the free exercise of the
function entrepreneurial activity that continuously records trade relations or market prices of the past and seeks to make an assessment and find out what future market prices will be, acting accordingly and helping to create through this action the actual formation of future prices.
Following the words of Mises himself, written in 1922: "It is the entrepreneurs who create the information according to which everyone adapts his affairs and who, therefore, directs their commercial operations" 13 .
The foregoing considerations do not prevent us from thinking that the pioneering work of Mises of 1920 was still far from the refined and purified contributions that Hayek and Mises himself would have realized in the following decades, and that would culminate with the development of the analysis of the entrepreneurial function and of information creation processes. Hayek learns from Mises the
'subjectivist' character of science and economic action, even if this will never allow him to share that underlying utilitarianism he
reproaches to Mises.

13 LV Mises (1922).

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On the other hand, it is necessary to remember that Mises' initial contribution was still very much influenced by an antecedent Marxist environment to which he wanted to respond and which led him to highlight in his analysis both the necessity of the use of money and the existence of prices to make economic calculation possible.

1.5 I NOBEL 2007: HURWICZ, MYERSON AND MASKIN

The intuitions of Hayek and Mises regarding the problem of incomplete (asymmetric) information are very important to understand that the efficient allocation of resources can not be achieved through the free market.
Only in conditions of complete and symmetrical perfect information, the necessary and sufficient incentive to make the individual decisions of the agents determine the efficient allocation of resources is given by the market prices: each price acts in fact as an efficient signal of scarcity for that particular resource.
Until the 1960s, the market was seen on one hand in its ideal version or general principle, the only one able to guarantee efficiency and on the other as a real market, conditioned by multiple imperfections, called market failures.
A first attempt to explain the different sources of market failure is known as the principle of the incompleteness of market structure: the common cause that the market fails is to be found
in the lack of one or more markets where you can make
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all those transactions mutually beneficial that, if carried out, would allow the efficient allocation of resources, simply by creating missing markets.
Unfortunately, the principle of incompleteness does not explain why new markets created to "complete" the structure should in turn be exempt from bankruptcies, therefore subject to externalities 14 and information asymmetries 15 thus creating new holes in the structure itself.
The information problem was solved by the theory of the design of the mechanisms, first performed by Leonid Hurwicz in 1960 and perfected by Maskin in 1977 and by Myerson in 1982.
The three theorists were awarded the Nobel prize in 2007 alone, as a testimony of the fact that the theory is constantly evolving. The central intuition of mechanisms design theory is that in order to solve this problem in all cases really significant, the constraints on agents' incentives to participate in a system (for example the market) are just as important as the constraints on available resources. To avoid the failure of the Market in a
context of, for example, information asymmetry, it is necessary to give to the

14 There is an externality when the behavior of someone affects the welfare of others directly and not through changes in market prices. In particular, there is a negative externality when someone's behavior causes damage to others and a positive externality when it provides an advantage to others.

15 We speak instead of information asymmetry when a condition occurs

which information is not shared entirely among the individuals involved in the economic process, so a part of the agents involved has more information than the rest of the participants and can benefit from this configuration.

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agents adequate incentives to share the information in their possession and commit to the execution of contracts.
The design of mechanisms (MDT) teaches not to seek the solution only in the markets that, as we have seen, can be incomplete in the structure, but in all the institutions. Each institution can be seen as a mechanism in the way of making economic decisions based on known information that can influence agents' incentives.
The mechanism design theory then analyzes how institutions and social organizations are structured so that they produce the desired effects.
To show the importance and the deep connection between the institutions and the incentives to the agents, Roger B. Myerson cited a dialogue of the Symposium of Xenophon 16 in which Socrates interviewed a model citizen who has two primary objectives: going out for his farm in
campaign to monitor and motivate its workers and then return to the city, where its participation in various political institutions is essential to maintain its rights to own this farm. These concerns about agents' incentives and political institutions play a central role in economic theory today, but they have not always had it in history.
As we have seen, however, in the early twentieth century,
economics theorists (Barone 1908, Lange 1938, Mises 1920, Hayek

16 Xenophon (between 384 and 360 BC). Socrates tells the young Critobulo a conversation he had with a rich landowner, Isimaco, on how to administer the assets.

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1935) have engaged in a heated debate on the possibility that a socialist reform of economic institutions would be possible without loss of economic efficiency.
We have also seen how the theories of the time did not provide sufficient elements to corroborate their respective theses on this vital subject in the history of economic thought.
In order to allow the analytical comparison of fundamentally different forms of economic organization, a new and more general theoretical framework was therefore necessary. Hayek (1945) had already argued that the key to this new economic theory should have been the recognition that economic institutions of all kinds must serve an essential function: to communicate information dispersed about the desires and resources of different individuals in society. From this point of view, the various economic institutions must be compared as mechanisms for communication.
Hayek also claimed that economists that the mathematical economists of his time were particularly guilty of not considering the importance of communication in market systems. "The economic problem of society is not just a problem of
how to allocate the resources given ... It is rather a problem of how to obtain the best use of resources present in any member of society, whose importance is relatively known only by these individuals. . it's a problem the use of knowledge because
you do not know in their entirety.
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This fundamental problem has been overshadowed by recent economic theories in particular from the use made of mathematics that acts as a filter that obscures economic principles. "(FV Hayek (1945)," The use of knowledge in society " , Page 86).
But the fundamental questions about social reforms and the validity
of institutions required a new fundamental social theory; in this research the abstract generality of mathematics had to be particularly useful.
In reality, the failure of the social reform theories perceived by Hayek was not due to the use of mathematics per se, but it was evident that there was a need for new fundamental mathematical-economic models. Among the mathematical economists who accepted this challenge indirectly launched by Hayek, Leonid Hurwicz has long been the leader, as well as the father
of mechanism design theory.
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CHAPTER 2

THE CONTRIBUTION OF LEONID HURWICZ

2.1 BIOGRAPHICAL NOTES

"I can not tell you the story of my life and what I did without talking about politics 17 ".
Leonid Hurwicz was born in Moscow on August 21, 1917 after the
Kerensky revolution in February but before the October Bolshevik revolution. In the early months of 1919, after the communists took power in Russia, he and his family returned to Warsaw, to his father's home. "My father was convinced, I rightly believe, that if
he stayed in Russia, he would have had serious problems with Lenin," says Hurwicz. "Of course, this is not my memory, I was only 14 months old, but I know that we have traveled with various makeshift vehicles, like chariots and horses, to get to Poland." 18
His father was a lawyer, a graduate of the Paris Sorbonne; in Warsaw he went for a five-year internship as required by legal practice, where he taught history in the meantime. Hurwicz's mother was a teacher too, but after the outbreak of the war she stayed at home with him and his younger brother giving them
lessons in reading, writing and arithmetic. Hurwicz began the

17 L. Hurwicz (2008).

18 A. Bauer (2008).

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school at the age of nine, until he entered a private institution attended and composed mostly of Jews.
It was a time of devastation throughout Europe, even though he and his family were not directly swept away, Hurwicz does not remember serious racial episodes in his youth. One year the University of Warsaw decided that the Jewish community had not helped to provide its share of cadavers to the medical school, so a group of students tried to force Jewish students to sit in a separate section of their classrooms.
Jewish students, including Hurwicz, remained in the back of the room for a whole year in protest. The protest succeeded and in the following years the Jewish students again sat down normally:
"I have experienced harassment during this period, but I have
never been beaten or assaulted personally and with my professors I have never felt discriminated against."
He graduated from the University of Warsaw in 1938 in law, originally with the intention of following in his father's footsteps. However, starting from his second year of law, he had followed some compulsory economics courses and had become more interested in this discipline than any other. "I was convinced that many problems observed on the European continent were due to politicians who could not understand economic phenomena," says Hurwicz. "Even if they had good intentions, they did not have the right skills to solve the problems."
When Hitler came to power in Germany,
Easterners warned: they felt like intruders in their
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countries, around there were horrible voices about the persecution. Hurwicz's father, sensing that the political picture could worsen very quickly, suggested his eldest son to study at the London School of Economics, rather than instituting a law practice in Warsaw.
Leonid went to London in the autumn of 1938, but in the spring of 1939 the British state refused to extend his visa.
Hurwicz moved to France and then to Switzerland with a transit visa. He arrived in Bern in August 1939, less than a week before Germany attacked and occupied western Poland, including Warsaw.
Hurwicz, hearing the news, did not know if his parents and brother had managed to escape to eastern Poland occupied by the Russians. In the spring of 1940, his parents were arrested and taken to a labor camp in an Arctic region of European Russia. He spent months in Geneva, enrolled as a part-time student at the university, living with little money and hoping to receive news of his family. In the end, Hurwicz contacted his cousins ​​in Chicago, as his parents told him they would help him if he needed to leave Europe.
In 1940, at age 23 and only in the world, but with some cousins ​​he had never met and an address, Hurwicz booked a ride on an Italian boat. "In a month, not less, Mussolini joined Hitler". So his ticket was useless, because no
Italian ship could enter American ports.
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"It was bad luck for me, because I did not have the chance to get reimbursed, and even if I had the money, how could I travel from Switzerland to some city that was not controlled by Hitler and then come to America ? ". Eventually he found a way: an airline opened a link between Geneva and Barcelona, ​​both neutral cities.
Hurwicz was thus able to fly to Spain and take a train to
Madrid, then Lisbon. He spent almost two months in the Portuguese town of Estoril, which was like a sort of "Monte Carlo" where he could tutor the children of wealthy Spanish and French families on holiday, shortly after I boarded a Greek boat, the Nea Agllas, succeeding so to get to New Jersey.In
Chicago he lived with his cousins ​​in the Polish section of the city, sleeping on their couch and following courses at the University of Chicago with the famous economist Ludwig von Mises. offering a job at the Massachusetts Institute of Technology from another well-known economist:
Paul Samuelson.
The work consisted of teaching and research assistance for only one semester: "A term that no self-respecting doctor would accept", says Hurwicz today. "But I have not had any other offers, in fact it has already been a miracle to get this job He moved to Massachusetts and began working as an assistant for Samuelson, who would have won the Nobel Memorial Prize for Economics in 1970. At MIT, Hurwicz developed a theory
on how companies calculate prices for their goods and services. .
31
He returned to Chicago in mid-June 1941, as now more than qualified candidate for an academic appointment again, world events made their progress.
After Pearl Harbor was bombed in December 1941, Hurwicz went to his professor of statistics and asked how he could help the war effort. The professor, engaged in the search for a new invention called radar, took him with him to work on the project.
This interest led him to the Institute of Meteorology at the University of Chicago, where Hurwicz documented the statistics of the army and navy recruits, but also of mathematics and physics necessary for the analysis of meteorological data.
Back in Chicago, he hired a young Wisconsin meteorologist, named Evelyn Jensen, with whom he married in July 1944. The first of their four children was born two years later.
Hurwicz worked for a short academic period at Iowa State University and then for another period at the University of Illinois. But in the early months of 1951, with rampant McCarthyism on university campuses, his politically liberal colleagues from
the economics department were targeted, and Hurwicz resigned in protest. Soon after, hearing a friend from Iowa who had moved to the north, Leonid decided to consider the proposal of the
department of economics at the University of Minnesota.
32
Within a couple of months, Hurwicz moved his family to Minneapolis, where he would develop the idea that would win him the Nobel Prize in Economics.

2.2 MATHEMATICS AT THE SERVICE OF THE ECONOMY

"When we talk about the economic process of a company, we sometimes focus on two variables," says Hurwicz. "One is the monetary variable, but then very often we assume the other variable as the underlying provision, the perfect competition, which means that people do what they should do, but in reality, there is usually some chapter on the manuals of economy, not too long, that tells you that there are different mechanisms that operate in particular in every economy ... My question was: what other systems or mechanisms and variables are possible? "
Hurwicz not only reflected on the question, but used mathematics to create economic models. He developed the design theory of mechanisms to help companies and other organizations to arrive at solutions that combine truthfulness, individual rationality and social well-being.
"There are two types of games in economics," says Hurwicz, "One is the game where people only use legal moves, then there's the real game, the one in real life, where people make moves and
strategies and in where some cases perform illegal gains. So
33
you must take into consideration that when you write the rules of the game the players try to cheat. "
This is the basis of the "design of mechanisms", for which Hurwicz, Professor of Economics at the University of Minnesota, won the Nobel Memorial Award 2007 in Economics 19 shared with Maskin and Myerson. Too frail to make the trip to Sweden, Hurwicz received the award from the Swedish Ambassador for the United States to the University's Ted Mann Concert Hall on December 10, 2007. She died on June 25, 2008 at the age of 91 in a Minneapolis hospital, where he was undergoing dialysis.

2.3 THEORETICAL CONTRIBUTION

The basic premise behind Hurwicz's theory may seem obvious now, but when he started working on it in the 1960s, the idea that gamers would favor by all means their own interest in commercial transactions was considered to be cutting edge because until then it had not been considered in the models. At the base of his theory there is the belief that incentives can encourage players to get the best possible result, not only for themselves but also for the other players in the game 20 . The work of Hurwicz of 1960 21 is part of the
historical debate on the comparative merits of the economic systems examined in the
first chapter. The main participants in this debate as we have

19 Nobel Foundation (2007).

20 Nobel Foundation (2008).

21 K. Arrow, J. Kenneth and L. Hurwicz (1960).

34
previously seen were Barone (1908) and Lange (1938) on the one hand, and von Mises (1920, 1935) and Hayek (1935, 1945) on the other.
In a polemic against the naive dreams of a socialist paradise, Mises (1920) had argued that competitive market equilibrium prices were necessary for the efficient allocation of resources. Against this thesis, Barone (1908), Lange (1938) argued that the efficient allocation of resources could be coordinated equally well by value indices set by a Socialist Planning Ministry.
Mises (1920) and Hayek (1935) expressed great skepticism about the feasibility of such central economic planning without the prices being determined by the competition, but their thesis on this point did not go into specific and focused mainly on the complexity intractable problem of resource allocation.
It is difficult to be convincing with these arguments of intractability; After all, if the economy is too complex for our analysis, then how can we be sure that a perfect competition market will find an efficient solution, or that a socialist planner will not be able to find one? For a convincing argument, a simple economic model was needed in which socialism (appropriately defined) could be shown to be less efficient than capitalism.
Naturally, the end of the twentieth century provided "empirical" evidence
with the fall of socialism.
35
The economics theorists today have realized what was missing in the old debates: the economists of the past could model constraints of resources, but not the incentive constraints. Hayek and others have elaborated some arguments that actually show a basic awareness of incentive problems, but their arguments have remained purely rhetorical without logical or mathematical support, in the absence of any general theoretical framework of reference for the analysis of incentives. .
In particular, Samuelson (1954) 22he had argued that no viable mechanism could guarantee an efficient allocation of public goods, because asking a person to pay for public goods according to his advantages creates an incentive to conceal his benefit. This observation seemed consistent with the general view that efficiency is only found in private markets, where competition acts as a mechanism for balance.
Trying to formalize this topic, Hurwicz found that the same incentive problems arise in the allocation of private goods. Once the necessary conditions for perfect competition have been met, he has shown that, with a finite number of individuals, no mechanism compatible with incentives is able to guarantee a Pareto-efficient allocation.
With this result, Hurwicz provided for the first time a general framework with which to analyze the significant issues of this
debate. He acknowledged the fact that information on the

22 P. Samuelson (1954).

36
economic situation, which allow or limit the economic possibilities, such as the endowments of resources and stocks of goods, the preferences of individuals for goods, are private information, known only to economic agents.
It is obvious, but it is worth stressing, however, that economic agents who move within the economic context, not observing the general aspects of the environment, can not have enough information to guide their actions, unless that information they are not communicated by an external element (the mechanism) that directly observes the context.

2.4 WHAT IS A MECHANISM

The mechanism is like a machine that collects and processes received messages, thus aggregating the true or false private information provided by many agents. Each agent strives to maximize his expected payoff (utility or profit), and may decide not to share disadvantageous information or send false information (hoping to pay less for a public good, for example).
In this context, markets and market institutions can be compared with a wide range of alternative institutions. Initially, much of the interest was focused on information costs and calculation of mechanisms, leaving out the problem of incentives. In many situations, providing incentives for
agent participation is an important part of the problem.
37
In order to better understand how important it is to provide incentives for the participation of agents, a small negative example will be presented.
Everyone knows the story of Solomon's judgment. Not everyone knows, however, that the judgment of Solomon is a problem of mechanism design. The story of Solomon's judgment is as follows: two women present themselves in the presence of the king with a newborn that everyone claims as their own; both women justify their claims by citing real or presumed facts. Solomon listens to all the arguments, but finds himself faced with a very difficult choice: it is not at all easy to know which of the two women has told the truth, because to know it is necessary to know information known only to ladies (private information).
As a result, they will have no interest in confessing the truth if it involves the loss of the child. The king then invents a ploy: announces that the child will be cut in half and
will be given a piece to every woman. Hearing this, the first woman declares she is not the real mother, while the second is in agreement to cut the child in half.
Thus Solomon understands that the true mother is the first woman, because no mother would ever allow the death of her child. Technically, her son's death would have been more inconvenient for her than assigning the child to the false mother.
Perhaps, however, the artifice that Solomon had engineered was so cunning, but it would not have been a winner if the second woman had chosen to
disregard the child too. If we assume that the judgment of
38
Solomon is a game, it would have two balances: the two women claim both the child or the two women both repudiate the child.
It is worth questioning why Solomon's stratagem is not so ingenious. The flaw is that Solomon's stratagem is not compatible with incentives or the two women are not motivated to tell the truth. Fortunately for the king, the second woman was too foolish to argue such subtlety and all went well.
Mechanism design theory became relevant to a wide variety of applications only after Hurwicz (1972) introduced the key concept of mechanism compatible with incentives, which allows to analyze and incorporate private information.
In particular, it allows a rigorous economic analysis in which the agents are selfish and have relevant private information.
In 1978, the formulation of the so-called principle of detection and the development of the implementation theory 23 led to great progress in the design theory of mechanisms. The principle of detection greatly simplifies the analysis of the problems of the design theory of mechanisms. On the basis of this principle, the
researcher, when looking for the best possible mechanism to solve allocation problems, can refer to a
small subclass of mechanisms, the so-called direct mechanisms.

23 E. Maskin, P. Dasgupta and P. Hammond (1978).

39
The direct mechanisms are not to be understood as a description of the institutions of the real world, but as relatively easy to analyze mathematical structures.
Optimizing the set of all the direct mechanisms for a given allocation problem is a well-defined mathematical process and once the optimal direct mechanism has been found, the researcher can translate the mechanism from the mathematical to a realistic phase. With this method of connection, the researchers
were able to solve some problems of institutional design that otherwise would have been difficult to handle.
This leads to the notion of "implementation" resulting as balance of the game of messages, where the mechanism defines the "rules" of the game.The comparison of alternative mechanisms is then used to identify the balance of the associated game of messages. optimal for a given objective function (such as a profit at a given vendor or social welfare), the researcher must first define the set of possible mechanisms, then specify the criterion of balance that will be used to predict the behavior of the participants.
Suppose to focus on a series of "direct mechanisms", where agents report their personal information (for example, their willingness to pay for a public good).
We can not assume that the agents will tell the truth, because from
rational agents they will be sincere only if it is in their interest.
40
On the basis of all these individual reports, the direct mechanism assigns an outcome (for example, the available quantity of public good and the expenses for its financing).
Now suppose we use the concept of equilibrium of the dominant strategy as our behavioral criterion. In game theory, a strategy is said to be dominant for a player if, whatever the choice made by the other players, it gives the player who performs it a better result than any other strategy. The hypothesis of rationality provides that a player who has a dominant strategy available to use it.
The notion of incentive-compatibility Hurwicz (1972) can now be expressed as follows: the mechanism is compatible with incentives if the agent's dominant strategy is to report information truthfully. Furthermore, it is possible to decide to impose a constraint on participation in the mechanism: no agent should worsen his situation by participating in the mechanism. That is: staying out, not joining the mechanism (be it a contract, an institution or something else), is not convenient.

2.5 THE TECHNICAL CONQUEST OF HURWICZ Hurwicz (1972) demonstrated the following, fundamental, negative result: in a pure exchange economy, no mechanism compatible with the incentives that meets the participation constraint can produce Pareto-optimal results.

Considering that not even a market system, under conditions
of incomplete information, can be incentive-compatible and
41
lead to an efficient allocation in the Paretian sense, a centralized allocation system that imitates the system of prices characteristic of the planned systems, will not in no way be more efficient. From this conclusion, a whole series of new questions and issues arise that have given other economists the opportunity to further develop the theory underlying the proposal by Hurwicz.
Since the work of the Russian economist has shown that there can not be an incentive-compatible mechanism leading to a first-best result, the question that has driven research studies in the field of the design of the mechanisms after his contribution becomes: What are the other criteria that can allow a resource allocation mechanism to achieve the best possible result in terms of efficiency? It is here that Roger Myerson's contribution is fundamental: the so-called Revelation Principle.
As already noted, the set of mechanisms by which a mechanism can be chosen is a formal element in the Hurwicz approach. One way to think about the problem is to interpret the choice of economic organization as a problem of constrained optimization. In this vision, there is a set of alternative incentive mechanisms, each necessary to meet certain structural constraints (for example, privacy preservation), a set
of environments, an objective function and, for each candidate mechanism, real costs ( in terms of resources) to execute this
mechanism.
42
Thanks to the mathematical model of the design of mechanisms we should be able to choose which mechanism of the real world is closer to the purely abstract and unreachable case of perfect competition. Hurwicz's theory is precisely this, very general and concerns the efficiency of any type of institution or mechanism of the real world. For example, it can be used to analyze the meticulous rules contained in a work contract or the rules by which a community decides itself and how many public goods to produce. The key to the success of the mechanism design theory is its extreme versatility.
The starting point of the theory is to represent each institution as a non-cooperative game and to compare the different institutions by comparing the results in terms of efficiency of the balances of the respective games. But how to reduce the complicated mechanisms of the real world to a simple game? The answer comes from Eric S. Maskin who introduces the principle of implementation, along with the contribution of Roger Myerson. Both will be analyzed in the next chapter.

2.6 DEVELOPMENTS OF THEORY

Hurwicz's works are so important that they allowed the development of different theories and models that deserve mention. As previously described, under some hypotheses Hurwicz (1972) has shown the following negative result: in a pure exchange economy, no mechanism compatible with the incentives
that satisfies the participation constraint can produce optimal Pareto-
43 results
. In other words, the presence of private information precludes full efficiency.
Hurwicz introduced a formal model of a communication process that incorporates this constraint, a dynamic message exchange process modeled on the Walrasian tâtonnement. In the Walrasian model, in fact, trade in goods takes place only when an equilibrium price has been reached that ensures the perfect coincidence between supply and demand: this price is formed only as a result of changes in demand and supply at different levels of prices. Taking again the Walrasian example, one could imagine the existence of a hypothetical auctioneer who starts trade between operators only when a price has been set that ensures the perfect balance between supply and demand.
The mechanism of tâtonnement has often been criticized above all on the basis of the idea that in no market exists a subject that has all the information that allows to reach a situation of equilibrium, so that often exchanges take place at non-equilibrium prices. Hurwicz used the term privacy (suggested by the inability of an agent to observe the private information of another) to refer precisely to this restriction. Instead of the direct exchange of goods, Hurwicz's attention is
however focused on the exchange of information that is a prelude to the exchange of goods. His model includes as a formal element, a
language used for communication.
44
The elements (words) used in this language are resources of "flow matrices" that shape the production and exchange of goods between agents.
Hurwicz imposed restrictions on the language and functions used to model the communication process, in order to generalize the properties of the competitive mechanism that one wants to achieve. In the 1972 work, he also acknowledged that the dispersion of private information between economic agents can create incentive problems. Finally, he formalized this class of problems by introducing game theory 24in the mechanisms, and also the concept and analysis of compatibility of incentives in the mechanisms. In the model of game theory the essential premise is that everyone must be aware of the rules of the game, and be aware of the consequences of every single move. The move, or the set of moves, that an individual intends to do is called "strategy". Depending on the strategies adopted by all players (or agents), everyone receives a pay-off (payout, payment, but also outcome).
Although the original formulation includes a tâtonnement as an exchange of messages, attention is focused on a static profile, that is, on the task of recognizing the balance of message exchange processes, rather than on the task of finding equilibrium. In
this literature, the verification scenario isolates the problem of
recognizing equilibrium.

24 JV Neumann and O. Morgenstern (1944).

45
In a test scenario, each agent reacts to an announced message by saying yes or no. The answers verify the proposed balance when all the agents say yes 25 .
This formulation allowed Mount and Reiter (1974) 26 to
provide a mathematical characterization: they consider the mechanisms that achieve a given objective or function 27 . Marschak and Radner (1971) and Radner (1972) subsequently adopted a different approach to the design of mechanisms, called team theory 28 .
The collective action takes the name of team [or team] when:
a) all those who participate have different information on the decisional context: b) the exchange of information involves a cost; c) all the collaborating people share a common goal that coincides with the interest of the group. Despite the sharing of a common objective, the decision of each component aimed at achieving the maximum collective result also depends on the decisions of others.
Interdependencies require the coordination of the decisions taken individually; this in turn requires the sharing of information (centralization), with the related communication cost,
or the setting up of decentralized decision-making mechanisms

25 In the computer language, a verification scenario is a non-deterministic algorithm.

26 K. Mount and S. Reiter (1974).

27 Realizing is the term used to refer to a situation in which the results of the

mechanism are precisely those specified by the objective function, when i

Agents do not attempt to use their private information strategically, but the term implementation is used when agents behave strategically.

28 VS Fumás (2012).

46
that, at any point in the organizational structure, allow partial use of information. The choice between centralization or decentralization of the mechanism depends on the advantages of the decisions taken, being able to count on greater information about the costs that the transmission and processing of information require.
In summary, Leonid Hurwicz, through his 1972 essay, determines a turning point in the economic theory of MDT. The incentive aspect comes to play a pre-eminent role which gives rise to the modern analysis of the mechanisms with Myerson and Maskin, in which it is assumed that the rational agents participating in the mechanism are endowed with private information.
In his essay, Hurwicz also demonstrates a negative result: there is no mechanism for allocating resources, different from the mechanism of perfect competition, but in any case consistent with individual rationality, capable of achieving allocative efficiency. If no real-world allocative mechanism is able to lead us to efficiency, which of the various mechanisms is still the best capable of generating the highest possible level of social well-being? This question becomes the heart of modern MDT. They will be Myerson with the principle of revelation and Maskin with the theory of implementation to provide valid criteria to choose the best mechanism. The possibility of answering the question
posed by Hurwicz is the keystone for the spectrum
potentially infinite of mechanisms design applications.
47

CHAPTER 3

ROGER MYERSON AND ERIC MASKIN

3.1 ROGER B. MYERSON

Roger B. Myerson was born on March 29, 1951 in a comfortable suburb of Boston with an excellent public school system, in a family that has always appreciated reading and scientific learning. His father did research and engineering in the production of artificial teeth a family business, and each of his parents returned to school at different times in his life to specialize.
The concern about the risks of a new nuclear war was widespread in the fifties, and like many boys of his generation, he was aware of this terrible threat from a young age.
Roger thus tells 29: "I have early memories in which I tell my father that I was worried about the political cartoons that represented the possible consequences of the Suez crisis of 1956, my father reassured me saying that the leaders of the world were using all their wisdom and intelligence to manage the crisis in
a peaceful way ". This perspective suggested to him that perhaps it would be

29 Nobel Foundation (2008).

It
was better if our leaders could have even more wisdom and understanding, to provide us with a guide to a safer and more peaceful world in the future.
At the age of twelve he became interested in science fiction, in particular a novel that depicted a future where advanced mathematics of social science provided the guidelines for a new utopian civilization. It was natural to hope that fundamental advances in the social sciences would be helpful in finding better ways to deal with the problems of the world, as fundamental advances in physics had been able to dangerously raise the stakes in the nuclear conflict. These ideas will accompany him throughout his life. As we will see later, Myerson has somehow managed to achieve them thanks to an extremely versatile economic model.
Arriving at college, he chose to devote himself to economics and applied mathematics even if he was not sure what was his way until he discovered the theory of games in 1972.

3.2 THE BIRTH OF INTEREST FOR THE THEORY OF GAMES

In the spring of 1972, as a Harvard student, Myerson participated in a decision-making course of Howard Raiffa that taught him to see the functions of personal utility as measurable aspects of decision-making that are expressed in
everyday life . At the end of the course Raiffa explained that the analysis of the
49
interactions between two or more rational agents (whose decisions maximize initial usefulness) is called game theory and described game theory as a field in which only progress had been made. limited. These observations then focused on the subsequent studies of Myerson. He felt that if he did not know how to analyze such fundamental models in the decisions of social life, he could not pretend to understand anything in the social sciences.
There were no regular courses on the theory of games at Harvard, and so he began to do independent research on the subject in libraries, looking for books and relevant articles. His main form of intellectual elaboration was to scribble notes in the margins of photocopied articles written by industry leaders: Robert Aumann, John Harsanyi, John Nash, Thomas Schelling, Reinhard Selten, Lloyd Shapley, and others.
Later in 1976, he was hired as assistant professor of the Managerial Economics and Decision Sciences (MEDS) department of the School of Management of Northwestern University (later Kellogg), in the 70's, game theory was a relatively narrow field and few schools had considered to have more than one game theorist in their faculty, but Northwestern has always been convinced of the importance of this economic-mathematical theory.
The MEDS department was probably the only academic department in the world where game theory in economics was not seen as a secondary topic, but as a
strength of the department.
50

3.3 FIRST WORKS

Myerson's early work was largely cooperative game theory, including the results of the doctoral thesis. Cooperative game theory begins with the assumption that people agree on some feasible outcome that is efficient, meaning that there is no other possible result that all the collaborating people would prefer. But in most situations we can find a wide range of efficient allocations, which represent better alternatives for each of the different individuals. An equitable bargaining solution should identify an efficient result, in which each individual obtains a utility that is in some way commensurate with his contribution to bargaining.
In several early works that were based on graduate school studies, Myerson showed how simple principles of fairness between pairs of individuals could be constantly extended to situations in which many individuals cooperate in coalitions.
All that Myerson has done in game theory has always been motivated by the long-term goal: to develop a coherent general methodology for game theory analysis. His idea of ​​game theory could not have
developed without a basic finding, that there may be a simple class of models that is generic enough to describe all the complicated game situations we would like to study.
Some fundamental questions about the role of information e
Incentives in economic systems were in the air at
51
Northwestern in the late 1970s. There was great interest in Leonid Hurwicz's ideas of compatibility with the incentives. These ideas have influenced Myerson in the search for a theory of cooperative games with incomplete information, together with the vision of such games with incomplete information in the general framework of the Harsanyi Bayesian model. After he learned the first version of the revelation principle for the implementation of Alan Gibbard's dominant strategy 30 , Myerson became one of several researchers who sought to naturally extend it to the realization of Bayesian equilibrium within the framework of Harsanyi's approach.
The principle of disclosure basically says that, for any balance of any communication system, a reliable mediator is able to create an equivalent communication system where honesty is a rational balance for all individuals. With the principle of revelation, we can generally apply some mathematically simple constraints that summarize the incentive problems, to convince people to share their information honestly.
Myerson wrote an article showing how the principle of revelation compatible with incentives in a Bayesian equilibrium could simplify the model of Harsanyi and Selten (1972) 31 , on the
bargaining solution for two-person games with

30 The so-called Principle of Revelation makes it possible to simplify the search for "agreements" or "mechanisms", or "contracts" appropriate in cases of bargaining with private assessments.

31 JC Harsanyi and R.Selten (1972).

52
incomplete information. This idea was the basis of the article on the principle of revelation, published in Econometrica in 1979 32 . Subsequently, thanks to the discussions with Robert Wilson and Paul Milgrom on the mechanisms of the auctions, Myerson began to realize that there could be much more interesting economic applications of its principle. He realized that the principle of revelation could be used as a general tool for achieving any unity of well-being, in any situation
where there is a problem of obtaining information from different individuals. During a visit to the University of Bielefeld in Germany (1978/79), he wrote an article 33in which he applied these ideas to the problem of designing an auction, where the goal is to maximize
the expected revenues of the seller, subject to incentive constraints, to get potential buyers to disclose information about their willingness to pay. When he returned to Northwestern, he worked with colleagues on other important applications and extensions
of these ideas. With David Baron he worked on the optimal regulation of a monopoly with private information on costs 34 .
Instead, together with Mark Satterthwaite he realized efficient mechanisms for mediation in bilateral exchange, that is, the exchange that involves a seller and a potential buyer for a single
indivisible asset.

32 R. B. Myerson (1979).

33 RB Myerson (1978).

34 See chapter 4.

53
With some simple assumptions, Myerson and his co-authors were able to obtain powerful theorems that show how the profit expected from any kind of individual who has private information you can obtain it from an analysis of sales expected from other like-minded individuals. In this calculation, an individual's profit depends on how
his private information affects the final allocation of assets, so people who have private information may be able to earn information revenue in any market organization system, that is, where the allocation of activities depends on their information.
The problem of providing incentives to people to honestly share private information is known as the problem of adverse selection, but it was not the only incentive problem that economists were learning to analyze in the 1970s. There was also growing literature on problem of providing incentives to individuals to choose their own "hidden" actions appropriately, a problem called moral hazard.
It is a form of opportunism that can lead individuals to pursue their own interests at the expense of the other party who can not verify their behavior. Robert Aumann (1974), in his definition of correlated balances for communication games,
.

35 RJ Aumann (1974).

54

3.4 PRINCIPLE OF DETECTION

In 1982, Myerson wrote an article 36 where the principle of revelation is extended in a unitary way to the problems of moral hazard and of adverse selection, thus elaborating a general theory of coordination systems compatible with the incentives
for Bayesian games with incomplete information . In the definition of Myerson the principle of revelation is "any equilibrium outcome of
an arbitrary mechanism can be replicated by an incentive-compatible mechanism". Given any real mechanism, the equilibrium obtained from the rational behavior of the participants can be simulated by a hypothetical direct detection mechanism (DRM)
that is a) equivalent as a result of the original mechanism, b) compatible with the incentives, and c) in which a reliable mediator operates that centralizes communication and that makes obedience and honesty are rational strategies of the participants.
On a strictly analytical level, a DRM is a relatively simple object to manipulate, because it is generally represented by
a system of linear inequalities. But, as is evident, it is a purely ideal construction: in the real world DRM simply does not exist.
However, the revelation principle tells us that for any equilibrium of any mechanism there is an equivalent DRM compatible with incentives. Therefore through the analysis of the
properties of an appropriate and mathematically traceable DRM,

36 RB Myerson (1982).

55
we can characterize without any loss of generality the outcomes of every possible mechanism, avoiding the otherwise insoluble problem of having to directly model the latter under conditions of informative asymmetry.
The set of mechanisms compatible with the incentives includes all the balances that can be obtained by adding any communication system mediated to the given game, and therefore this mechanism can be used by an arbitrator or a leader to design the system of communication.
The principle of revelation states that any rational balance of any individual behavior in any real social institution mustbe equivalent to a theoretical coordination plan compatible with the incentives. Given all possible informative reports from individuals, the equivalent incentive-compatible plan
simulates results in cases of lying and disobedience in the original mechanism, as illustrated in Figure 1. Thus, without loss of information, a mediator can plan honesty and
obedience as the best policy for all.
56 By Bengt Holmström, Myerson published an article in 1983 37

on how the economic concept of efficiency should be extended to situations in which people possess private information. According to the basic concept of Pareto efficiency, the economy is efficient when there is no way to improve the position of any agent without worsening another's position. But when we admit that every individual can have different private information we have to rethink many parts of this definition.
The economic assessment of efficiency or inefficiency may therefore depend on information that is not available to the public, and a realistic conception of the feasibility of a social choice must take into account incentive constraints as well as resource constraints. Thus, the concept of efficient incentive should be applied to the whole mechanism depending on the type of private information known
only to individuals.

37 B. Holmstrom and RB Myerson (1983).

57
Holmström and Myerson have essentially suggested that a mechanism compatible with incentives should be considered an efficient incentive when there is no other mechanism compatible with incentives where the expected utility for each individual is greater. This extends the traditional concept of Pareto to the general case of private information.

3.5 RECOGNITIONS FOR THE THEORY OF GAMES

From the 1980s onwards Myerson focused on writing a general textbook on game theory, which was published in 1991 38 . In this book he presented the general methodology of analysis of game theory which, together with many other theorists, had helped to develop over the years. Other game theory texts were published in the early 1990s, and textbooks on economic theory have begun to deal with game theory: the information economy and the design of mechanisms have become essential parts of microeconomic analysis. In October 1994
the importance of game theory in economics was sealed by the Nobel Prize Committee, with its award to John Nash, John Harsanyi and Reinhard Selten 39.
At the end of the eighties, Myerson started working
on the application of models of game theory in politics

38 RB Myerson (1991).

39 The three economists were rewarded for "their fundamental analysis on

balance in the theory of non-cooperative games ".

58
economic. He had always thought that the applications of the theory should go beyond the traditional sphere of the economy: in constitutional democracies, constitutions and electoral systems define the rules of the game with which politicians compete for power. The game theory approach should be particularly useful for understanding how changes in these constitutional structures can influence the behavior of politicians and the welfare goals achieved by the government. For example, in an article on the comparison of electoral systems with Robert Weber 40 he elaborated different models to evaluate the competitive implications in electoral reforms.
Analysis of games with incomplete information has shown economists how the probabilistic analysis of decision uncertainties is able to offer practical insights into competitive strategies. So Myerson also wrote a textbook on probabilistic models for economic decisions that was published in 2005 41 .
As the late twentieth century approached, Myerson began to wonder if progress in the analysis of competition could effectively encourage the hope of a better twenty-first century. The point was whether recent advances in political and economic theory could offer a better framework for
understanding many practical problems of institutional design.

40 RB Myerson and RJ Weber (1988).

41 RB Myerson (2005).

59
He realized that the progress that seemed to offer the most interesting insights to improve international relations is largely based on the ideas of Thomas Schelling and Reinhard Selten, in particular on the focal point effect 42 and on the analysis of strategic credibility 43 .
Thus, when America decided to invade Iraq in 2003, Myerson applied Schelling's ideas about deterrence to show how American rejection of military containment could exacerbate threats against America. When a powerful nation uses its own military force without clear limits, instead of deterring potential adversaries, it can actually motivate potential opponents to invest more in counter-military resources.
Thus, he argued that the world's greatest superpower may need to set clear and credible limits on the use of its military force, according to rules and principles that the rest of the world can judge.
In the search for the universal principles that underlie all kinds of institutional structures, Myerson has managed to understand that incentive problems and the reputation of political leaders are critical and fundamental factors for the creation of any political institution. The rules of every political system must be executed by
government officials , and implementing these rules is a gambling problem

42 In game theory, the focal point is a solution to which people tend spontaneously even in the absence of communication or agreement, because to them

it seems natural, special or relevant.

43 The premise is to eliminate the balances that imply threats or

unbelievable promises.

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moral. Incentives for lower government officials depend on prizes and punishments that are controlled by the highest political leaders.
Thus we find, in the heart of the state, a problem of moral hazard whose solution depends on the individual reputations of political leaders. The institutions of any political system are organized by political leaders, whose first imperative is to maintain their reputation in front of their loyal supporters. The problem of cultivating a democracy can therefore be seen as a problem of creating opportunities, for which politicians start to cultivate a good democratic reputation, that is, a reputation as voters' delegates.
As an application of these ideas, he criticized US policies for establishing democracy in occupied Iraq, arguing that the first priority of the occupation authority in 2003 should have been to establish elected and well-funded local councils, in which local leaders throughout the country would start building its independent reputation as responsible for democratic governance.
In 2007, the Sveriges Riksbank Prize in economics in memory of Alfred Nobel was awarded to Leonid Hurwicz, Eric Maskin, and Myerson. The latter said: "I am very proud to have linked my name to Leonid and Eric in such an important way, and to the progress in the analysis of the coordination mechanisms and incentive constraints to which we have contributed
along with many other great economists; the opportunity to share
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this honor with my wife and my family and celebrate with many friends and colleagues was a wonderful experience for me, but I understand that the real winners are the ideas of incentive analysis and
design of mechanisms, and I want to continue working to understand these ideas more deeply and to be able to present them more clearly.
There is still a lot to learn about how our social institutions work, and how they can be better designed " 44 .

3.6 ERIC S. MASKIN

Eric S. Maskin 45 born in New York City on December 12, 1950, from a Jewish family but grew up in Alpine, New Jersey. With less than a thousand inhabitants, Alpine was a village too small to have its own secondary schools, so he attended middle and high school in the city of Tenafly, three miles from Alpine.
In Tenafly, Maskin had as a calculation teacher Francis Piersa, who opened his eyes to the suggestive beauty of mathematics. Thanks to him, he became an important mathematician at Harvard, where he studied algebra with Pierre Samuel, Richard Brauer, George Mackey and Lars Ahlfors. Almost by chance, he participated in an "information economy" course held by Kenneth Arrow. The course was a mix of unconventional topics
of economic theory, but a good part of it was dedicated to

44 Nobel Foundation (2008).

45 Nobel Foundation (2008).

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work by Leonid Hurwicz in the nascent field of mechanism design. This work was for Maskin a revelation: he had the precision, the rigor, and sometimes the beauty of pure mathematics and he faced problems of real social importance; an irresistible combination for him.
In fact, Maskin finished college by doing essentially with a doctorate in applied mathematics, but Harvard's applied mathematics program at that time was extraordinarily flexible, and allowed students to study what they wanted, as long as they wrote a thesis that they had a "significant mathematical content". Maskin I was able to follow several courses of
economy (although no one, to his regret, in macroeconomics and economic history), including the course on the general equilibrium of Truman Bewley, where he got to work with his classmate and then future co-Nobel laureate Roger Myerson , and the analytical seminar of Jerry Green, in which also participated future great economists such as Elhanan Helpman, Bob Cooter, and Jean-Jacques Laffont.

3.7 THEORY OF IMPLEMENTATION

Becoming a research fellow in Cambridge, England, Maskin was interested in a problem inspired by the work of Leonid Hurwicz, the so-called "implementation problem": under what circumstances it is possible to design a mechanism (that is, a procedure or game) that implements a specific social goal (formally a
social choice rule) to achieve Nash's equilibrium? After
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've struggled with this problem, he was able to understand that the condition of monotonicity (now called "monotonicity of Maskin") was the key: If a social choice rule satisfies monotonicity, then it is not possible to implement a Nash equilibrium 46 .
The proof of the goodness of the intuition was when he mathematically demonstrated how an implementation mechanism could be explicitly designed. In reality the mechanism is rather complex and articulated and the details of its results are in the article "Nash Equilibrium and Welfare Optimality" 47 .
Eric Maskin closed the circle traced by Myerson with the principle of revelation. Thanks to the implementation theory, he has succeeded in providing a criterion for choosing the best of the various equilibria in the event that a real mechanism can be represented by more than a hypothetical direct detection mechanism, each with its own equilibrium.
Maskin extended Hurwicz's ideas in another direction. Indeed, many mechanisms are subject to the problem of the multiplicity of possible results. This is an obstacle to the predictive power of the mediator: if many results are possible, but I do not know which is the most efficient, it becomes very difficult to structure a mechanism, for example to finance public goods. Maskin then posed the problem
differently: if I can get many results, and only some of them

46 The Nash equilibrium represents the situation in which the group of players comes to be found if each member of the group does what is best for himself, ie aims to maximize his own profit regardless of the choices of the opponents.

47 E. Maskin (1999).

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these are efficient, then my goal is to find which restrictions to the rules of the game I have to impose in order to reach only the efficient balance (this branch of the mechanism design has taken the name of implementation theory).
Kenneth Arrow previously worked on social choice theory in a similar context. The social choice rule is a rule that selects one or more alternatives from a set, based on the preferences of individuals (for example: simple majority). While Arrow focused his studies on how a specific social rule was able to represent truthfully or not the will of a group of individuals, from 1970 onwards the scholars' attention shifted to the strategic behaviors that agents could adopt on several occasions. , depending on different social choice rules.
Following this line Maskin in his article "Nash Equilibrium and Welfare Optimality" argues that: "If individuals know the rule by which the planner selects alternatives on the basis of reported preferences, they may have an incentive to report falsely". One wonders, therefore, if it is possible to devise a mechanism, or a voting rule, which encourages voters to truthfully express their preferences on a set of alternatives.
Two economists have worked on this question in particular: Gibbard, with "Manipulation of voting schemes: a general result", (1973) and Satterthwaite with "Strategy-proofness and Arrow's
conditions: Existence and correspondence theorems for voting
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procedures and welfare functions" (1975) 48. The two managed to prove that if a set contains at least three alternatives, then there is no social choice rule that can be implemented in a mechanism in which revealing one's real preferences is a dominant strategy.
This result, which is applied both in the processes of production of public goods, and in the voting procedures, is called in literature the theorem of the impossibility of Gibbard and Satterthwaite.
The theorem only confirms, in a different context (strategic, instead of the normative-axiomatic), what was already known in the economic theory of social choice rules due to the impossibility theorem of Arrow 49. This result shifted the attention of scholars to what is known today as the implementation problem. One wonders, in essence, if it is possible to create a voting procedure in which all the balances of the game
(understood as equilibriums of Nash), achieved through this procedure, are efficient. While Groves and Ledyard (1977) 50 and Hurwicz and Schmeidler (1978) 51 showed that in certain situations it is possible to construct mechanisms in which all Nash equilibria are
efficient in the Paretian sense, Maskin showed that, so that
a balance of Nash was necessary that

48 A. Gibbard (1973), MA Satterthwaite (1975).

49 K. Arrow (1951). It says that, given the requirements of universality, not imposition,

non-dictatoriality, monotonicity, independence from irrelevant alternatives, it is not possible to determine a voting system that preserves social choices.

50 T. Groves and J. Ledyard (1977).

51 L. Hurwicz and D. Schmeidler (1978).

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a fundamental condition was respected: the condition of monotonicity (Maskin monotonicity).

3.8 MASKIN MONONICITY AND HARVARD'S YEARS

Maskin's condition of monotonicity states that "If an alternative to ∈ X is selected by
any voter's preference ordering, then a must still be selected" (E. Maskin (1978) , "The implementation of social choice rules", Colchester, University of Essex, Dept. of Economics ).
To fully understand Maskin's condition, let's imagine a group of individuals who will soon be called to vote for the construction of a public work. Their preferences on the different projects depend on which "state of the world" occurs before the vote: for example, an individual could choose to vote for the construction of a school, rather than a nightclub, if he was waiting for the birth of a child (otherwise he would prefer and vote for the construction of a disco).
In this scenario, the voting rule satisfies the Maskin Monotonicity if, and only if, it ensures that the project being voted is built in a constant and determined state of the world or if the latter varies (in our example the individual has a child) the project always remains the one chosen without undergoing alterations
due to the change in the state of the world.
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The results achieved by Maskin were developed by many other economists such as: Postlewaite and Schmeidler 52 , Palfrey and Srivastava

53 , Mookherjee and Reichelstein 54 and Jackson 55 , which generalized the results achieved by Maskin for games with complete information, to games with incomplete information.

Entered in 1977 in the MIT department of economics, Maskin has met and worked with the likes of Paul Samuelson, Franco Modigliani or Bob Solow. He then moved on to work for Harvard (1985), in what seemed to him the most natural place for the kind of long-term work he was doing.
The theoretical group formed at Harvard at that time, with Andreu Mas Colell, Jerry Green, Oliver Hart, Drew Fudenberg, Mike Whinston and Marty Weitzman, was something extraordinary and unrepeatable in the history of the economy.
The meeting with heterodox theorists Janos Kornai and Amartya Sen, from which
Maskin learned about the themes of central planning and the subtleties of social choice theory, helped him in his theoretical evolution.
Maskin in his autobiography 56 refers many times to "luck". He claims to have been particularly fortunate in the first place
to have discovered the economy, secondly to have entered the

52 A. Postlewaite and D. Schmeidler (1986).

53 TR Palfrey and S. Srivastava (1989).

54 D. Mookherjee and S. Reichelstein (1990).

55 M. Jackson (1991).

56 Nobel Foundation (2008).

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research in a time when the mechanism design began to flourish, and, more importantly, to have had a succession of teachers, students, colleagues and friends in the profession overtime. Finally, in a world where so many people do not like their jobs, they were lucky enough to spend their
days working hard on something they love.
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CHAPTER 4

APPLICATIONS

4.1 INTRODUCTION

The Mechanism Design Theory, although it may seem composed of mostly abstract concepts, is a theory that lends itself well to a large number of practical applications in different areas, and that represents a clear and efficient solution to the problems caused by the presence of
information asymmetries affecting institutional and economic systems. Mechanism design theory analyzes how economic and social institutions are designed to achieve desired goals.
The practical applications of the theory are extremely numerous and can range from the analysis of purchase and sale transactions to that of the supply of public goods and voting mechanisms, from the study of remuneration incentives within companies to that of regulatory mechanisms. Further applications concern the optimal design of auction procedures, that of taxation rules, bank regulation or the differentiation of the range of products offered on the market (versioning 57 ) and of the respective prices for a private company that
intends to maximize the own sales revenues.

57 A tool that allows multiple programmers to develop the same software and at the same time manage the evolution of the same.

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In this chapter I will present various examples of the possible applications of the mechanism design theory, as conceived by Hurwicz, Myerson and Maskin, whose Nobel Prize is therefore the recognition of an extremely important research topic, both from the point of view theoretical both for its numerous applications and which is still demonstrating its vitality today.

4.2 THE CASE OF PUBLIC GOODS

The applications of the theory of mechanisms are extremely numerous and precisely its abstractness and extreme generality determines its possible application in the most diversified fields. Essentially they are situations in which the optimal decision to be made depends on information that is not public. Information is instead decentralized, and to make optimal decisions it is necessary to collect this information. What makes the problem complicated is that those who have information have their own interests, which do not necessarily coincide with those of society.
Mechanism design theory tells us if it is possible, and, when possible, how to do it, to formulate the appropriate incentives for agents who pursue their own interests to reveal their information truthfully.
In a public economy, a common problem is how to make decisions about the production and financing of public goods. This
problem represents an excellent field of application of the theory.
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Suppose, for example, that the construction of a road between two countries is proposed, we do not know if it is really worth building the road, ie we do not know if the monetary cost exceeds the monetary benefits for the inhabitants of the two countries. The first thing that can come to mind is to ask the inhabitants of the two countries what their monetary benefits are, determining the decision to build and the
form of financing on the basis of such statements, but if the problem is approached in this naive way it is doomed to failure. It is normal to assume that, for example, if the inhabitants of a country announced that the road has a high value for them, then they
would have to pay more. In such a case, they would be tempted to announce a lower value than the real one, in order to reduce the share of financing against them. Suppose then that yes
decides to charge a fixed quota to the two countries, regardless of the value they announce. This would be a distortion in the opposite direction: now the inhabitants would have an incentive to overestimate the monetary value that they assign to the road. By doing so they would make sure that the road is built with the highest probability, and would not pay any additional cost. One of the first applications of mechanism design theory has studied how to provide the appropriate incentives to reveal the truth in such situations 58 . Clarke and Groves have succeeded in demonstrating that, in the absence
of income effects on the demand functions of the public good, it is possible

58 E. Clarke (1971) and T. Groves (1973).

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build a mechanism such that the truthful disclosure of willingness to pay is a dominant strategy for each agent and that the level of equilibrium of production of the public good is such as to maximize social welfare.
By asking each individual to indicate their willingness to pay for a certain public good, the good will be provided if and only if the total willingness to pay indicated by the agents exceeds the
total cost of supply, ie if and only if the supply generates a social surplus equal to the total declared availability minus the total cost.
In the event that the asset is provided, the mechanism requires that each agent pay a contribution or tax equal to the difference between the total cost of supply and the total availability to pay revealed by all the other agents.
Each agent will therefore be encouraged to reveal his real willingness to pay (dominant strategy): underestimating or overvaluing it is not convenient, since the tax depends in any case on what the others declare.
The defect is that it generates a total of tax revenues always lower than the total cost of supply, even with this limit the mechanism shows that even in the absence of market prices the regulator can get the relevant information on the willingness to pay the economic agents and the problem informative of Hayek can be
solved even without recourse to the market.
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4.3 ELECTIONS AND FINANCE

In the political sciences, an eternally debated topic is how to design electoral systems. This problem can also be addressed through the theory of mechanisms.
Consider a simple example. There is a charge to be filled and three candidates A, B and C; the electoral system (the mechanism) simply asks to indicate the preferred candidate, and the candidate with the most votes wins (simple majority system). What could happen wrong in such a situation? Consider a case in which all citizens prefer candidate A, but have different opinions on B and C, some prefer B to C, others prefer C to B.
If I prefer A to B and also prefer B to C, how should I vote? Unfortunately, the answer is: it depends on how I expect others to vote. If I expect that no one votes, and therefore that A has no chance of being elected, then I will try to "limit the damage" by voting B, and the same will do all the others; but in this way the prediction "no one votes A" self-confirms, the voters all vote for their second choice and the first choice of all does not receive any votes!
Mechanism design theory studies how to choose electoral systems so that such undesirable situations do not arise. In this case, the problem can be solved by asking
voters to indicate the order of their preferences 59 .

59 E. Maskin and P. Dasgupta (1977).

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The classic problem of governance of the separation of ownership and control can also be studied as a problem of designing mechanisms.
The question is how to ensure that managers actually do shareholder interest by making decisions that maximize the value of the company. Here the source of the problem is that managers do not own the company, and therefore do not bear the costs and do not enjoy the benefits that result from their decisions. If they are paid simply with a fixed salary, regardless of the results, managers can make decisions that favor them (for example, hiring and nepotistically promoting staff) to the detriment of shareholders.
On the other hand, if managers are paid strictly based on the result, for example based on changes in the price of the shares, they risk putting up with them too much risk, as the share price may vary for reasons that have nothing what to do with what management does. Shareholders must therefore find ways to provide the appropriate incentives to managers without putting up with them excessive risks.
Mechanism design theory studies how to design the remuneration and career paths of management in order to
solve this problem.
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4.4 ECONOMIC REGULATION

A very interesting debate, which has been going on for a very long time and which is very close to the MDT, is economic regulation. Selznick (1985) 60 defines regulation as a continuous and concentrated control exercised by a public authority on activities that have value for the community.
In this context the mechanism design theory can be very useful to solve the debated topic of control of companies that supply and produce public goods and services (public utilities).
The main purpose of economic theories on regulation is indeed to justify and identify the appropriate forms of public intervention in the economy (regulatory approach). Part of the regulatory literature has proposed a more positive analysis, trying to explain why in some circumstances a regulated market can be observed (even if there is no reason for its existence from an economic perspective) or because inefficient forms of regulation.
The markets, according to the classic assumptions of freedom of entry and low access costs, perfect information and perfect financial markets, naturally converge towards a configuration of perfect competition. In many cases, some of these requirements are not fully met: natural or legal barriers and
structural costs can lead to market failures, which means that

60 P. Selznick (1985).

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markets are unable to converge towards an efficient allocation of resources.
Market imperfections can be numerous and of various kinds, for ex. natural or artificial monopolies, imperfect information, externalities and public assets, scarcity rents 61 or destructive competition. Externalities are often taken into account to justify regulatory intervention in the environmental field or sometimes in the telecommunications sector (eg, the regulation for the allocation of the frequency spectrum that I will cover later). Scarcity rents and destructive competition are concepts used more frequently by politicians and political scientists rather than
from economists. The scarcity rents are extra profits due to the particular scarcity of a resource, which can have an impact on the shares issued by an enterprise and also generate negative externalities.
At the same time, destructive competition is due to unstable forms of competition: short-sighted firms do not invest sufficiently due to the excessively risky environment in which they operate and this leads to long-term inefficiencies. The most frequent case of regulation, however, has to do with the existence of monopolies.
As is known, monopolies generate inefficiency and higher costs than a perfect competition market. The figure below shows the Marginal Revenue (RM), the
Marginal Cost (CM) and the business demand functions. The point of

61 JP Olsen, MD Cohen and JG March (1972).

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intersection between CM and the demand curve represents the equilibrium in perfect competition conditions (q *; p (q *)), while the monopoly equilibrium (q °; p (q °)) is given by the intersection of the CM and RM functions.
Consumer surplus is the area below the demand curve. The darkest area represents the so-called dry or net loss of well-being, corresponding to the decrease in consumer surplus net of changes in company profits (ie total surplus), which occurs with the transition from a market of perfect competition to a monopoly in consequence of the fact that the total quantity exchanged decreases and the equilibrium price increases.


Whenever a market failure occurs, a loss of well-being is observed; obviously the purpose of the social planner is the maximization of the overall well-being, which
implies the minimization of the aforesaid loss.
78 From
a regulatory perspective, to justify regulation, however, it is not sufficient to demonstrate that a market failure has occurred: it is also necessary to prove that public intervention is capable of improving the free market equilibrium.
Among all the achievable public interventions able to increase well-being, it is necessary to select the one that allows the maximum increase of social welfare. Even if, among all the feasible public policies, regulation of a market is the most efficient way to cope with a certain market failure, it should however be stressed that many alternative ways have been proposed in the literature to deal with such a hypothesis.
For example, in the presence of externalities, the Coase theorem 62 states that private bargaining would be sufficient to internalize all the gains and costs provided there are no transaction costs. Furthermore, the use of Pigouvian subsidies and taxes 63, or a redefinition of property rights and the creation of new markets, could be alternative ways of dealing with market imperfections.
In general, what matters is not to understand whether public intervention is efficient or not; the regulation is justified not so much by the fact
that through it the failures are completely eliminated

62 RH Coase (1960).

63 The Pigouvian Tax is a method of governing polluting emissions created by the English economist Arthur Cecil Pigou. It is a tax, per unit of product, charged to the producer subject of externalities.

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of the market, but because it is possible to increase efficiency more than any other alternative remedy.
In a classical reference context, that is to say in conditions of perfect information and in the absence of transaction costs, regulation is not always necessary, since it is possible to reach the optimal solution (first-best) without resorting to it. However, by introducing a more real scenario, regulation could be a desirable solution because, for example, it could be less expensive or lead to fewer distortions.
The rationale for regulation derives from the fact that the principal (ie the social planner or the regulator) has divergent objectives with respect to those of the agent (the regulated enterprise). It is frequently assumed that the company seeks to maximize its profits or its stock value; more generally it maximizes its surplus. The purpose of the regulator can be to achieve some social and political objectives (such as, for example, the diffusion of a certain service on the whole national territory), to guarantee certain technical requisites or to achieve certain economic results.
In practice, regular means introducing some rules and certain constraints aimed at conditioning the agent's behavior in
order to achieve a better economic result.
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4.5 TYPES OF REGULATION

The first attempts at regulation were of the "command and control" type. They consisted of the explicit imposition to the economic agents of the maintenance of a specific conduct. Policies such as the cost of service regulation 64 (which recognize a rate of return on invested capital) belong to this type of regulation.
The cost of service regulation essentially attempts to impose on the company a price equal to the average cost, calculated on the basis of the cost of capital. In order to estimate this, the regulator takes into consideration the debt burden and the yields of bonds with a risk similar to that of the regulated entity. Subsequently the regulator sets the price
in order to ensure the company profits, but limits them to a given percentage of the capital invested.
Instead of fixing the price, the regulator can choose the rate of return that the company is allowed to have. This type of regulation leaves little power to the regulator and presents another important limit defined in literature as the Averch-Johnson effect 65 : the company has little incentive to produce efficiently. More specifically, managers could be incentivized to over-invest in physical capital at the expense of the labor factor, thereby increasing the marginal cost of capital. Furthermore, this
method does not provide adequate investment incentives for the

64 RE Braeutigam and JC Panzar (1993).

65 A tendency towards overcapitalization, which can be found in companies operating under a natural monopoly regime and trying to increase their profits, against a regulation that sets a net maximum at their unit rate of return (to the ratio of profits / capital).

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reduction of production costs. Finally, the regulator often does not have many important information needed to implement such a policy. This implies that, even if it is able to perfectly control the behavior of the company, it may not know what is the optimal policy to be adopted.
A different method of regulation, which also reduces the regulator's power over the enterprise, is the so-called price cap. The price cap consists in placing a ceiling on the price charged by the company. The term price cap is also used when the regulator is not allowed, or can not in any way, to observe the costs of the company. A more efficient version of the price cap method consists in setting a price for a limited time horizon, revising it at a later stage in order to extract as much surplus from the company as possible.
The main advantage of the price cap regulation method is that to implement it the regulator does not necessarily need to observe and measure the economic result of the company. Furthermore, by making sure that the company claims the right to appropriation on the extra profits deriving from the reduction of costs, the regulator provides the company with the right incentives.
The price revision allows the regulator to extract a larger surplus. In general, the price cap is increased in line with the rate of inflation and decreased in relation to technological progress (with the consequent reduction in costs) and when
possible to some specific factors of the company.
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The price revision generates a problem of commitment and one of a temporal order. The problem of commitment is due to the fact that, at the time of renegotiation, the regulator unilaterally modifies the parameters and can extract all the extra profit deriving from the reduction of costs. For the regulator it is therefore difficult to commit oneself credibly not to renegotiate the maximum ceiling for a given period of time. The temporal problem stems from the fact that frequent revisions reduce the company's incentives to be efficient, as the cost reduction effort becomes less profitable.
Proposing sporadic revisions may not be credible and may result in the risk of leaving the company too high a surplus. A further limitation lies in the fact that the company, to increase the gross profit margin (mark-up), could be encouraged to reduce the quality.
To solve at least the problems of timing and credibility, the regulator can propose an income sharing clause (earnings-sharing clause). The clause implies that, in each revision, the cost reduction is calculated and the new price fixed so as to share the incremental profit between the company and the regulator on the basis of some predefined distribution rule.

4.6 INCENTIVE REGULATION

Nell’ultimo decennio è emerso un altro metodo di regolazione che differisce dal tradizionale ‘"comando e controllo", Invece di vincolare il comportamento di un’impresa, l’incentive regulation mechanism
consiste nel fornire all’impresa i giusti incentivi (in modo che i suoi
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obiettivi si avvicinino maggiormente a quelli del regolatore), lasciandole la libertà di scegliere come attuarli. In qualche misura il metodo di regolazione del price cap può ritenersi un precursore della incentive regulation66.
Questo cambiamento nel modo di regolamentare è certamente una conseguenza della difficoltà riscontrata nell’osservare le caratteristiche di un’impresa e nel controllarne il suo comportamento, a causa dello svantaggio informativodi cui il regolatore o police maker soffre67.
In the past, the nationalization of companies was the typical approach used to deal with natural monopoly cases. It was then thought that the nationalized enterprises would maximize social welfare. In other words, managers were asked to charge a price equal to the marginal CM cost even if this involved a financial loss (since in this market configuration the average cost is higher than CM). This loss, according to classical economic theory, should have been financed through fixed sum taxes (lump sum). This way of reasoning implies not only that managers are rational and benevolent, but also that they have perfect
information about the performance of the cost function (which is not

66 PL Joskow (2006).

67 The well known informative problem of Hayek.

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almost never occurs); it is also known that the lump sum 68 taxes are not feasible.
Setting up a private company can raise problems different from those analyzed so far. As noted above, a manager of a public company might even find some
difficulty in assessing the real costs of your business. It is even more difficult for the regulator of a private company to obtain this information. Moreover, one of the tools used by the social planner, when the company is nationalized, is to subsidize the monopoly through taxation. This is absolutely not feasible for a private company. Likewise, obtaining the government subsidy or even asking the company itself to deliberately generate losses (that is, practicing prices equal to the CM) are hardly feasible solutions.
Transfers of money from the government to the business are more likely to be allowed in the event of a contract. In simpler terms, this occurs when the government is the only consumer of the asset (this is the case, for example, of companies that produce arms).
When the law authorizes transfers, two very common regulatory contracts are "fixed price" and
"reimbursable cost plus fixed compensation" contracts (cost-plus-fixed-fee).

68 A lump sum tax is a fixed sum tax with a tax requirement a factor exogenous to the individual. It therefore provides for a monetary transfer. Its peculiarity is that the tax is neutral as regards the behavior of consumers and producers, since it does not modify in any way the

balances of a competitive market both seen in partial equilibrium, and seen in

total balance. It is the only type of tax that does not violate the conditions of Pareto efficiency.

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The first consists in fixing the price of an asset at a level sufficiently high to prevent the undertaking from incurring losses. The second consists of two components: the costs are fully reimbursed and, in addition, a fixed fee (independent of the economic result) is transferred to the company. One could
also construct a contract that is a combination of the two, that is, a total cost shared between the company and the government, and a fixed transfer.

4.7 SOLVE THE HAYEK INFORMATION PROBLEM

In reality, the regulator or "police maker" collides with the inevitable informative problem of Hayek, that is, with the lack of information for the public authority regarding the market conditions, the costs of the company, its technology, etc. Below we will examine some regulatory mechanisms that take into account the information asymmetries between the regulator and the company's managers. Furthermore, the problem of commitment, as well as that of imperfect information, have led economists to look for new and more powerful schemes that take into account developments in the literature on the subject.
of incentives and principal-agent models. According to the Bayesian approach to regulation, the regulator can not observe some important variables and functions (such as the demand function, the marginal and fixed costs of the company, or both types of costs) and
instead bases its behavior on certain convictions. which elaborates to
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priori about these variables.
The authority then uses these convictions to calculate its expected utility and then maximize it. In this context, the problems of adverse selection are common (the regulator does not know the real cost structure of the company) and moral hazard (the regulator can not observe the effort made by the company to reduce its
costs). The problem arises of how to intervene to regulate a company when such information is incomplete or completely absent.
The question is fully part of the theory of the design of mechanisms: as in the case of a public good, we have a police-maker who wants to maximize social welfare and to
do this must induce an agent in possession of private information to reveal credibly his information.
It is evident that it is not enough to ask the information to who owns it, because in the presence of any criterion of regulation of the
price based on production costs the monopolist will always have an incentive to reveal a higher production cost than the real one, so as to induce the regulator to set a higher price and thus increase profits.
In an essay from 1979, the economists Loeb and Magat 69 hypothesized a scheme to fix the price that solves the information problem. The essence of the regulation mechanism proposed by
Loeb and Magat consists in allowing the monopolist to choose

69 M. Loeb and WA Magat (1979).

87 of
its price and the commitment to the authority to provide the company with a subsidy equal to the surplus that consumers get at the price chosen by the company. It is evident that the mechanism puts the monopolist in front of a trade-off: raising the price means on the one hand increasing profits but, on the other, reducing the consumer surplus and therefore the subsidy received from the regulator; vice versa in case of price reduction the opposite solution will occur.
Starting from this essay, the modern literature of MDT has developed a very thorough analysis of the regulation processes of natural monopolies. The central idea is that regulation can be treated as a game with incomplete information between the authority and the monopolist, a game whose solution passes precisely for the identification of a mechanism capable of inducing the credible transmission of information and the adoption efficient behavior by the monopolist.
Using the principle of revelation, authors like Baron and Myerson
1982 70 and Sappington 1983 71they designed optimal regulation mechanisms under general conditions. The terms of the question remain those analyzed above: the policy-maker wants to extract the largest possible surplus from the monopolist, but at the same time must provide an adequate incentive for efficiency; all this in terms of information asymmetry and respecting the constraint of

70 DP Baron and RB Myerson (1982).

71 D. Sappington (1983).

88
participation of the monopolist, to which it must however agree remain on the market.
The model of D. Baron and R. B Myerson (1982), and D. Sappington (1982), sets the problem as an asymmetric information game, within which the regulator is unable to observe either the type of technology that the company employs for the production of public goods, nor the level of commitment of management in reducing costs. Also on this occasion the purpose of the theory is to look for a remuneration mechanism such that the company has an incentive to reveal this information truthfully.
For example, we consider that the total costs that the company faces are composed of: c = β - e, where βIt is a parameter that is indicative of the total cost of the technology employed by the company, while and is the level of commitment with which the direction cuts costs that burden on the company. In the situation in which the government does not know either the β parameter (classical parameter of the adverse selection) or the parameter e (classical parameter of moral hazard), a remuneration contract must be created for the production of the public utilities which incentivize the company to reveal the type of technology used in production, and to reduce production costs as much as possible.
The mechanism design theory, on this occasion, helps us to analyze the efficiency of different remuneration mechanisms such as: cost-plus contracts (ie the government
undertakes to repay the total costs of the company plus a fixed premium
89
), or fixed-price (which provides for a transfer to the company according to the β parameter communicated to the government).
Using game theory, the aforementioned scholars have found that consistent with the general result of Hurwicz (see chap.2) none of these remuneration mechanisms is incentive-compatible. In fact, a cost-plus contract encourages the company to truthfully reveal the technology used, but at the same time reduces those of employees to engage in work. In fixed-price contracts, however, the incentives for reducing total costs are strong, but at the same time the incentive to correctly reveal the technological equipment is eliminated.
company arrangement. Hence the economic theory has developed in many areas, one of which, developed by J.Laffont and J. Tirole, is the analysis of the effects on the efficiency levels of the company following the insertion of intermediate institutions between the enterprise and government (eg governmental agencies), with the sole purpose of limiting the level of information asymmetries 72 .
In conclusion we can affirm that the theory of the design of the
mechanisms has also revolutionized a field of investigation such as the control and regulation of market power that boasted an ancient tradition dating back to the nineteenth century.
In the pre-MDT literature the regulation process was analyzed in the context of ad hoc hypotheses, such as the existence of one
date production cost structure, often chosen for reasons of

72 J. Laffont and J. Tirole (1993).

90
mere analytical convenience, or the need for the monopolist to obtain a minimum return on capital, a return that was identified in a completely arbitrary manner. It is clear that, with these premises, any normative judgment on the various regulatory criteria was substantially unfounded.
By representing regulation as an incomplete information game, the MDT has allowed contemporary economists to base the various criteria, including some of the traditional ones, on rigorous theoretical grounds. This allowed a comparison no longer only arbitrary of the merits and defects of each criterion, and therefore the formulation of increasingly reliable regulatory judgments.
Let us not forget, however, that any regulation mechanism can not ignore the lesson of Hurwicz 1972 which is always valid and current. In the presence of private information, the first best is never reachable by any regulation mechanism, so it will be necessary to choose among the various second best mechanisms that judged best from the point of view of the objectives pursued by the
police maker.
91

4.8 A AUCTION MECHANISM FOR UMTS FREQUENCIES

Another practical application of the mechanism design theory that was used a few years ago is the auction for the sale of UMTS 73 frequencies by the Italian state.
The interest of the theory in relation to the UMTS topic is linked to the auctions carried out in Europe for the transfer of licenses on the frequencies used by this new technology. In the Italian case, on
10 January 2001 the Telecommunications Authority proceeded to formally award the UMTS licenses to five winning companies: Andala, Ipse2000, Omnitel, Tim, Wind, for a total sum of 13,815 million euros.
Since March 2000, more than € 740 billion has been spent in these auctions in the various countries of Europe. Despite this enormous movement of money there has been a great disparity in the distribution of earnings and offers at the level of nations.
Many controversies and accusations have arisen, due to the poor design of the auctions and the inadequate exploitation of economic resources. The accusation is that of having damaged the economic telecommunications market and therefore defrauded the
various States.

73 The Universal Mobile Telecommunication System (UMTS) is a multimedia mobile communication standard. This system allows new ones

terminals to split color images, movies, video broadcasts, e-commerce,

music and make video calls. Technology is also known as

"Third-generation mobile telephony".

92
The first auction for the sale of UMTS licenses took place in England in March and April 2000. This auction is certainly the most successful auction in Europe. Not only is it also the auction that historically gave the seller (in this case the British government) the greatest economic return, with a record of 39 billion euros.
The design of the applied auction model was studied and prepared within three years by Paul Klemperer 74. The main problem was that four licenses were originally available and there were already four major telephony giants on the market. The intent was therefore to avoid that new companies did not enter the auction for fear of the groups already present, since the latter, in addition to greater knowledge of the telecommunications market, already had a customer base and existing technologies that could be easily updated.
Klemperer proposed a new auction mechanism, the Anglo-Dutch auction, assuming an auction in which only one object is sold, proceeds in an ascending manner in which the price rises incrementally until there are only two contenders.
At this point the two contenders will make their offer in a sealed envelope that must be at least equal to the last offer made in the
previous phase .

74 P. Klemperer (2002).

93
This mechanism was later abandoned, as the British government opted for five licenses, and these five could only be sold to as many as five bidders.
In this way at least one license would end up in the hands of an incoming company and the cases of collusion would be reduced drastically. It was decided for a multiple ascending auction that involved in addition to the four signatures already present as many as nine new companies entering, establishing a total gain of 39 billion euros.
Only four months later, licenses were sold in the Netherlands. The context was similar to that in the United Kingdom and the government was inspired by it for the auction design. In fact, even here there were five possible candidates for five available licenses. Unfortunately there was not the same success: the new entrants, recognizing their position of inferiority, made contracts with the old managers.
In this way the auction design proved to be not very functional.
The only new entrant participating in the auction was Versatel who had to stop in the offers after receiving legal threats from the giant Telfort. Versatel, despite repeated appeals, was not heard by the government, because the latter wanted to avoid cash losses and therefore decided not to suspend the auction. The result was unsatisfactory and the Dutch government obtained a revenue of only
3 billion euros, compared to the 10 predicted after observing the British auction.
Despite the negative example set by the Netherlands, in October
of 2000 in Italy he did manage to avoid a failure
94
similar. Inspired by the English model, it was decided to add the rule that there could not be more licenses than bidders already on the market, and therefore probably the number of licenses would have to be reduced. This solution proved too optimistic and the various giants, aware of the previous auctions, intimidated the entry of other companies, reducing the number of participants to seven, of which six potential entrants (for six licenses) and only one external (Blue) that came eventually excluded.
The result was 14 billion euros compared to the 25 who had predicted. This Italian error could easily have been avoided with more time spent on the design of the auction design. Furthermore, this second failure showed clearly how the previously used model was not really robust if not adapted to the specifics of the various state markets.

4.9 BANK REGULATION

Another brilliant application of the theory of mechanisms that has been developed in recent years concerns bank failures and in general the solvency problems of banks, a topic that has become extremely topical.
Following a bank failure the authorities are faced with a choice or to make the institute bankrupt, with all the damaging consequences that derive from it or try to save it by restructuring it. An easy way to restructure a complex bank
was invented by two game theorists, Jeremy Bulow and Paul
95
Klemperer 75 , as well as confirmed by Willem Buiter who later became chief economist of what is perhaps the most complex bank in the world, the Citigroup.
Bulow and Klemperer have developed such an elegant mechanism that at first glance it seems a logic-based play of logic: the two theorists propose that regulators can forcibly divide a troubled bank into a good "bridge" bank and into a bank. "Survivor" bad.
The bridge bank holds all the assets and only the essential obligations, such as the money that individuals have placed in savings deposits or, in the case of an investment bank, the money deposited by other companies. The surviving bank does not hold the assets, but only the remaining debts; in one fell swoop the bridge bank is fully functional, has a good capital reserve and can continue to make loans, request and buy shares.
The surviving bank is obviously not a lost cause because the surviving bank is the owner of the bridge bank! Here is the second part of the mechanism: when the surviving bank fails and its creditors look at what they can save, part of the loot will include the actions of the still functioning bridge bank.
This should offer them better conditions than trying to
save themselves from the disaster of the original bank. In the meantime, the

75 J. Bulow and P. Klemperer (2009).

96
bridge bank will also continue to quietly support the course of the economic system.
Still on the subject of banking regulation, a further application of the MDT concerns in particular a mechanism that finally brings confidence to the center of the banking system, a rare and increasingly necessary element in a period when distrust in financial institutions has become the norm.
The purpose of the theory is simple and effective: we need to return to a market-based banking regulation system in which banks will no longer have full freedom as in the current system. In such a system based on the market we need to reassure the supporters that the institutions behave responsibly, thanks to a mechanism of regulation and control. The problem is that no economic operator is willing to believe that a regulator could allow a large bank to fail.
An excellent solution could be to change the rules on bank debts. A new debt contract, "equity recourse note" (ERN), is at the heart of the mechanism proposed by market veteran Jacob Goldfield and the usual two economists, Jeremy Bulow and Paul Klemperer 76. An ERN functions as a traditional bond, except that in times of difficulty, stress, interest payments would be made with the institution's equity rather than in
cash.

76 J. Bulow. and P. Klemperer (2013).

97
"Stress" is defined not by regulatory authorities, who may not appropriately report it for fear of generating alarmism, but from the price of the bank's shares. Let's say that if the share price is $ 40 when the ERN is issued, the limit price could be a quarter, $ 10. At any time,
when interest payments are due and the share price is below $ 10, the refund will be made in shares always at a nominal price of $ 10.
Banks in this way do not "fail". They will not be able to go bankrupt because it will always be possible to issue new shares and redeem ERN holders. Banks in times of difficulty will then automatically acquire capital guarantees in shares most traded on the markets.
There will be no traumatic moment in which large blocks of debt are converted into capital guarantees, causing problems and backlashes in other parts of the financial system. Only interest payments are converted into capital, and not all ERNs will be converted at the same activation price. Poorly managed banks will not collapse, but will be slowly hungry for requests by funds from disgruntled investors. The "too big to fail" will no longer be a factor and the banks will all be small enough to drown in their own bathtub if they do not behave fairly. Of course, investors would prefer to receive money, not stocks, so bankers should work hard to
prove their honesty and competence.
98
This mechanism is an ideal solution to restore confidence to an economic sector that has lost a lot in recent years, guaranteeing the principal value of social capital and not a system based only on equity instruments as now. Banking regulators should at
least make an attempt to follow the MDT in this field as well.
99

CONCLUSIONS

In the early twentieth century, economic theorists (Baron
1908, Lange 1938, Mises 1920, Hayek 1935) argued that socialist reform of economic institutions was possible without loss of economic efficiency. A careful analysis of their discussions has shown that the current economic framework has not provided sufficient evidence to support their thesis on this vital subject in the history of economic thought.
To allow the analytical comparison of fundamentally different forms of economic organization, we need a new and more general theoretical framework. Hayek in 1945 argued that the key to this new economic theory should be the recognition that economic institutions of all kinds must serve an essential function: to communicate information
dispersed about the desires and resources of different individuals in society. From this point of view, the various economic institutions must be compared as mechanisms for communication. Hayek also stated that the mathematical economists of his time were particularly guilty of not considering the importance of communication in market systems.
But fundamental questions about social reform require a new fundamental social theory. In this research the abstract generality of mathematics should be particularly useful.
The failure of the social reform theories of institutions perceived by
Hayek is not due to the use of mathematics per se, but this
100
shows that there is a need for new fundamental mathematical-economic models.
The intuitions of Hayek and Mises regarding the problem of incomplete (asymmetric) information are very important to understand that the efficient allocation of resources can not be achieved through the free market. Only in conditions of complete and symmetrical perfect information, the necessary and sufficient incentive to ensure that the individual decisions of the agents determine the efficient allocation of resources is given by the market prices: each price acts in fact as an efficient signal of scarcity for that particular resource.
Until the 1960s, the market was seen in its ideal version, or general principle, the only one able to guarantee efficiency. The real market on the other side was affected by multiple imperfections, called market failures.
The informative problem was solved by a brilliant theory called the design of mechanisms, first performed by Leonid Hurwicz in 1960, perfected by Maskin in 1977 and by Myerson in 1982, so much so that the three theoreticians were awarded the Nobel Prize. only in 2007 to witness the fact that the theory is constantly evolving.
The central intuition of the mechanisms design theory was that in order to solve this problem in all cases, the constraints on agents' incentives to participate in a system (for example the market) are just as important as the constraints on
available resources.
101
In order to avoid market failure as a general principle in a context of information asymmetry, it is necessary to give agents adequate incentives to share the information in their possession and to commit themselves to the execution of contracts.
The design of mechanisms (MDT) teaches not to seek the solution only in the markets that, as we have seen, may be incomplete in the structure, but in all institutions. Each institution is seen as a mechanism in the way of making economic decisions based on known information that can influence agents' incentives.
Leonid Hurwicz has provided for the first time a general framework in which information on the economic situation that allows or limits economic possibilities, such as the endowments of resources and stocks of goods, the preferences of individuals for goods, are private information, known only by economic agents. It is obvious, but it is worth repeating that economic agents who move within the economic context, not observing the general aspects of the environment, can not have enough information to guide their actions, unless such information they are not communicated by an external element (the mechanism) that directly observes the context.
The mechanism is like a machine that collects and processes received messages, thus aggregating the true or false private information provided by many agents.
Hurwicz introduces two types of constraints: the requirement for compatibility (for
each participant in the mechanism is dominant strategy reveal
102
their private information truthfully) and the participation constraint (for each agent is rational, that is more profitable, participate in the mechanism) . Each agent strives to maximize his expected payoff (utility or profit) given the two constraints, and can decide
not to share disadvantageous information or send false information (hoping to pay less for a public good, for example). In this context, markets and market institutions can be compared with a wide range of alternative institutions. Hurwicz (1972) has shown the following negative result: in a pure exchange economy, no mechanism compatible with the incentives that meets the participation constraint can produce Pareto-optimal results. The fundamental question then becomes: What are the other criteria that can allow a resource allocation mechanism to achieve the best possible result in terms of efficiency?
This is where Roger Myerson's contribution is of fundamental importance. The so-called Principle of Revelation (Myerson 1982) is the cornerstone of the MDT. It states that, given any real mechanism, the equilibrium obtained from the rational behavior of the participants can be simulated by a hypothetical direct detection mechanism (DRM) that is a) equivalent as a result of the original mechanism, b) compatible with the incentives, and c) in which a reliable mediator operates which centralizes communication and
which means that obedience and honesty are the
participants ' rational strategies .
103
The principle of revelation states that the equilibrium, therefore the efficiency result, of the DRM is completely equivalent to that of the original mechanism.
A DRM is completely virtual, but "simple" to analyze because it is "only" a set of compatibility and participation constraints that a hypothetical mediator interested in social welfare requires participants to obtain truthful information from them and non-opportunistic behavior.
Eric Maskin closed the circle traced by Myerson with his principle. Thanks to the implementation theory, he has succeeded in providing a criterion for choosing the best of the various equilibria in the event that a real mechanism can be represented by more than a hypothetical direct detection mechanism, each with its own equilibrium. The implementation theory (Maskin 1977) serves to "choose" the best of the different equilibria in case a real mechanism can be represented by more than one DRM, each with its own equilibrium.
Maskin has extended Hurwicz's ideas in another direction, in fact, many mechanisms are subject to the problem of the multiplicity of possible results. This is an obstacle to the predictive power of the mediator. If many results are possible, but I do not know which is the most efficient, it becomes very difficult to structure a mechanism (for example to finance public goods). Maskin then posed the problem differently: if I can get many results, and only some of these are efficient, then my goal is to find what restrictions
to the rules of the game I have to impose in order to reach only the
104
efficient balances (this branch of mechanism design has taken the name of implementation theory).
The mechanism design theory then analyzes how institutions and social organizations are structured so that they produce the desired effects. Thanks to its broad applicability to different areas of the economy, MDT is an
excellent tool for maximizing social well-being. Although it was born and developed in the last forty years, its potential has not yet been fully understood by economic operators, so much so that many do not even know its existence.
The theory of the design of mechanisms has finally become a topic of current affairs in recent years. Despite the
2007 Nobel Prize , it was gradually shelved due to its extreme variety of application that had ended up penalizing it.
This renewed interest was realized thanks to the great work done by Paul Klemperer, both as regards auctions, ERNs, and many other applications. It is certainly not a coincidence that, according to the well-informed, Klemperer himself is vying for a forthcoming Nobel Prize for Economics.
It is hoped that this renewed interest will be a good thing to solve the old problem of public goods that has never been definitively resolved, or at least to keep the debate alive on a fundamental topic for the life and credibility of an organism like the A state that is increasingly in difficulty and daily
mined in its foundations.
105
Finding a way to make the institutions more efficient, whether they are political, legal or economic, should represent the future of good state administration.
Mechanism design theory has shown us an easy way to achieve greater
common well-being . It is up to us, as it should be, to travel it or not.
106

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