What Thomas Schelling says about his divorce. Thomas Schelling. Micromotives and macrobehavior. Permanent address of this publication

In this book, 2005 Nobel Laureate in Economics Thomas Schelling examines systems of behavior in which an individual, in response to and adapting to external circumstances, is unable to understand how his seemingly insignificant and even seemingly meaningless actions, in combination with the actions of other individuals, give rise to unforeseen results and lead to significant unintended consequences for large groups. Thomas Schelling lived 95 years (1921–2016), and worked in the fields of game theory and behavioral economics. On the English language the book first appeared in 1978. This book is referenced by Daniel Kahneman in , Nate Silver in , Richard Thaler in .

Thomas Schelling. Micromotives and macrobehavior. - M.: Publishing house of the Gaidar Institute, 2016. - 344 p.

Download abstract ( summary) in the format or

Chapter 1. Micromotives and macrobehavior

This book explores the relationship between the characteristics of behavior individuals, constituting a certain social aggregate, and the characteristics of this aggregates. Sometimes knowledge of individual intentions is used to predict the behavior of aggregates. If there are several possible behaviors that could lead to the observed outcome, we must find data that allows us to choose one of them.

As a rule, all hypotheses use the notion that people have certain preferences, that they pursue goals, minimize effort or difficulty and maximize visibility or comfort, try to find company or avoid it, that is, they behave in one way or another in a special way, which we can call "targeted". In addition, goals or objectives are directly related to other people and their behavior. They may also be limited by an environment of other people pursuing their own goals and solving their own problems. Typically, we have some type of conditioned behavior—one that depends on what others are doing.

And if we know what problem a person is solving, and we think that he can actually solve it, and in doing so, we can also solve it, then we can predict what this person will do by putting ourselves in his place, and solve his problem in the form in which, in our opinion, he sees it. It is the method of "solving the other person's problem" on which microeconomics is largely based.

Of all the social sciences, it is economics that best fits the analysis I have described. In economics, "individuals" are people, families, farm owners, and so on. It often seems that a good deal of this unguided and undirected activity of individuals leads to cumulative results that are not so bad; moreover, almost as good as if someone took charge of these individuals, figured out what to do, and in doing so could make everyone do what he was supposed to do. Two hundred years ago, Adam Smith said of this system that it works as if some invisible hand was providing this coordination.

There is no reliable guarantee that the behavior of individuals, aimed at achieving their own goals, should usually lead to collectively satisfactory results. Economics is a special case—big and important, but special nonetheless. The method of analysis, generally accepted in economics, biology, and also in many other sciences not related to life, is the study of "equilibria". Equilibrium is a situation in which a certain movement, activity, adaptation, or reaction has stopped, bringing something to a stable, resting, "balanced" state.

There are many things that can go wrong with "equilibrium analysis", including the possibility that it oversimplifies things by neglecting adjustment processes, or exaggerates the importance of equilibrium by not noticing changes in the parameters that define equilibrium. But no one should resist "analysis of equilibrium" for fear that by admitting that something is in balance, he thereby admits that it is good.

The economy is a large and important special case, not a model for all other social phenomena. The economy is primarily concerned with transactions in which everyone involved voluntarily participates. Behind the typical free market are centuries of gradual development of property rights and other legal arrangements, and an astounding standardization of goods and services, as well as the terms that describe them.

Economists know many reasons why markets do not always work to everyone's satisfaction. People lack the knowledge to be able to price various forms of medical care, it is difficult to distinguish a good second-hand car from a bad one, or a sloppy repair from an honest one.

But let's now look at the activity that at first glance seems to be "market", but on closer examination it does not turn out to be such, namely the "non-market" of Christmas cards. I mean the situation of choosing to whom to send a postcard, which one, how expensive, by what date, with or without text. My superficial study of this issue indicates that there is a widespread, but not universally shared opinion that this system has certain features of a trap. Even people who like Christmas cards in general find parts of the system funny, ridiculous, and generally annoying.

The situation is not developing optimally for one simple reason: there is no reason for this. There is no mechanism that would direct individual reactions to one or another general result.

There were times when wise people believed that the planets should rotate in a circle. When observations finally proved that they do not rotate in a circle, the question arose - "what is the reason?" People have been trying to figure out what keeps the planets from spinning in perfect circles. It eventually became clear that, according to the laws of motion and gravity, there was never any reason why planets should be expected to be in perfect circles. The norm was not circles, but ellipses.

When we ask why the "free market" of Christmas cards doesn't lead to optimal exchange, the answer is that it's not the market, because there was no reason to expect optimal results from the start. The free market, when it works, is a special case of the conscious voluntary exchange of alienable goods. Only some ellipses turn out to be circles.

Chapter 2

There is a class of statements that are true of the totality, but not of individual elements, and this truth does not depend on how people behave. They are true for a closed system of behavior, but not for the behavior of every person and even, strictly speaking, not for certain groups that are smaller than the totality.

The situation is reminiscent of the game "musical chairs". Every player knows that if he does not hurry, he will be out of the game because he will not have time to sit down when the music stops. In economics, as in many other social sciences, we usually deal with a feedback system. And the feedback loop is usually one of those relationships that persists no matter how people behave. The output of one part of the system is the input to another.

Consider the puzzle: if the probability of having boys and girls for each couple is 50%, what will happen to the ratio between boys and girls if each family wants only a boy and stops having children as soon as it has its first boy? Half of the women will have boys at their first birth, and these couples will no longer have new children. Couples with girls will keep trying and stop only when a boy is born. How will the ratio of boys and girls in the population be distorted as a result?

But if you think about it, it becomes obvious that no "stopping rule" can affect the final proportions. In the first round, half of the children are boys. In the second round, only half of the families will have children, but half of them will also be boys. Half of the all-girl families will try their luck a third time, and according to the 50:50 distribution hypothesis, half of the couples will have boys and half will have girls. If every time half of the births are boys and the other half are girls, then, no matter when the process stops, there will still be equal numbers of boys and girls. (Another conclusion is that we know, without any addition, how many children will be born. Eventually each family will have exactly one boy; there will be as many girls as boys; and on average there will be two children per family. .

Chapter 3. Thermostats, Lemons, and Other Model Families

The home thermostat is an instructive device. This is the brain of the heating system. It controls the temperature by reacting to the temperature. The system that includes the thermostat is a model for many systems of behavior - human, vegetative and mechanical.

If the system is able to complete the task of reaching the desired temperature, it generates a cyclic process. In the morning, the temperature rises to the level at which the thermostat is set - and slips it. Then the temperature drops back to the set value - and drops below. It rises again and again exceeds the set value. The house never heats up just to the right temperature and stays there.

This chapter focuses on some families of models that are widely used in the social sciences.

Critical mass. In the social sciences, the term has been borrowed from nuclear engineering, where it is widely used in connection with atomic bombs. Critical mass models involve some activity that becomes self-sustaining after some minimum limit has been crossed.

In social relationships, the "critical number" usually varies from person to person. For example, you can participate in a campaign to support a candidate if there is any meaningful chance that he will win. Someone else - only if his chances are better than all other candidates, and I - only when it is almost certain that he will win.

In a dying seminar, it may happen that with any number of people present, two or three will consider that they are not enough; when they leave, two or three more will think that this number is not enough, and when they also leave, two or three more will think the same. The fact that in the end no one else does it does not give us any measure of how many satisfied participants were missing at each point in the trajectory.

Two special terms have come into use to distinguish subclasses of critical mass. One is a tipping point and the other is lemons. Model of lemons was first described by George Akerlof in an article. This economist claimed that the salesperson of a used car knew whether it was squeezed like a lemon or not; the buyer has to play averages, knowing only that some cars are lemons, but not knowing whether the one he buys will be a lemon. Buyers will only pay the price that reflects the average frequency of lemons in the used car crop. This average price is too high for a lemon, but it reduces the cost good cars offered on the market.

Owners of good cars are reluctant to sell them at prices that leave room for lemons that other people sell; therefore, good cars are less likely to appear on the market and the average frequency of lemons increases. When buyers find out about this, they leave even more room for lemons in the price they are willing to pay. Those machines that in the previous market were average quality machines are now undervalued. The desire of their owners to sell them has decreased even more. The percentage frequency of lemons continues to grow. Eventually the market may disappear, although institutional measures such as guarantees or certification of cars by dealers who use their reputation to sell good cars may keep the market alive.

Akerlof extended this model to a number of markets where there is unequal information from both sides.

Critical mass models can be explained using a family of graphs as an example. We count people for whom the critical number is 30 or 20, 1 or 75, and build a graph in which the height of the axis indicates how many people for whom the critical number lies between 20 and 25, 25 and 30, and so on (Fig. 1). The graph is nothing but this frequency distribution curve converted to cumulative form. It measures for each expected turnout number the number of people for whom the given number is large enough. It is "cumulative" because it includes, at any point on the horizontal axis, all people who are located to the left of that point in the original distribution.

Rice. 1. Graphical representation of the critical mass model

The line drawn by the dotted line, going at an angle of 45 °, shows equilibrium - if 25 people are expected to come, exactly 25 will come. When the curve and the dotted line intersect, equilibrium points appear.

Three more possibilities are shown in Fig. 2. Curve C shows a dozen people who will come regardless of turnout: the curve starts at 12 on the vertical axis. The turnout of those 12 will attract a few more people, and there is a steady balance at 16 or 18. If 25 or 30 people are expected, less than 25 or 30 people will show up and people will drop out until 16 or 18 people walk. We have an unstable equilibrium around 50% or another stable equilibrium again at 85.

Rice. 2. Variations of the critical mass model

Curve A reflects our dying workshop; critical mass cannot be reached. About a quarter of people will walk if half walk, half will walk if two-thirds walk, and two-thirds will walk if everyone walks. But not everyone will go. There is no self-sustaining turnout level.

On Curve B, critical mass is not a problem. Any expectation between zero and 70 will attract that number and more number, which converges to a single stable equilibrium where the curve intersects a straight line going at an angle of 45°. Expectations greater than 70 will not be supported and the process will converge on 70.

A few years ago, Garrett Hardin chose the now common name to describe a particularly common structure of motivation. He delivered a speech entitled "Tragedies of the Commons" which was published in Science.

"Public resources" has come to serve as a paradigm for situations in which people's pursuit of their own interests affects other people in such a way that they are collectively better off if they can be restricted, but no one benefits from individual self-restraint.

Examples are highways so clogged with cars that they move almost at the same speed as pedestrians on the adjacent sidewalks, a beach so crowded that people wonder why they came here, and a library so crowded that you might as well buy the books yourself.

A self-fulfilling prophecy. The general idea is that some expectations are of such a nature that they provoke the kind of behavior that results in the expectations being met (see also ). In the 1930s, when people believed that the bank was on the verge of bankruptcy, they rushed to withdraw their deposits and provoked the bankruptcy they feared.

Chapter 4 Sorting and Biasing: Race and Gender

This chapter is about the kind of segregation—or separation, or sorting—that can be caused by discriminatory individual behavior. By "discrimination" I mean the reflection of a conscious or unconscious concept of sex, age, religion, skin color, or some other factor underlying segregation, a perception that influences decisions about where to live, next to whom to sit, what choose a profession or, conversely, avoid, with whom to play or talk to. This chapter explores some of the individual incentives and individual perceptions of difference that can collectively lead to segregation.

Further presentation, in my opinion, is of interest to specialists who can refer to the original source.

The 2005 Nobel Prize in Economics was awarded to Israeli economist Robert Auman (University of Jerusalem) and American economist Thomas Schelling (University of Maryland) "for enriching our understanding of the nature of conflict and cooperation through the apparatus of game theory."

Aumann Robert (b. 1930) is a well-known economist and mathematician, born in Frankfurt am Main (Germany). After the establishment of fascist power, he emigrated to the United States with his parents. He received his secular and religious education in New York. In 1955 he defended his doctoral thesis in algebraic topology at the Massachusetts Institute of Technology. After working in the United States for some time in this specialty, he moved to Israel for permanent residence, where he created a school engaged in research on game theory and decision making.

Schelling Thomas (b. 1921), professor emeritus of economics and political science at the University of Maryland, emeritus professor of political economy at Harvard University, where he worked for over 30 years (1959-1990) and completed his Ph.D. The beginning of the vision of game theory as a unified construction for the social sciences was laid by T. Schelling's book "Strategy of Conflict" (1960).

Let us preface the concretization of the scientific achievements of R. Aumann and T. Schelling with the prehistory of the issue.

A major contribution to the general theory of uncorporate games was made by the Nobel laureates in economics in 1994 - the American economists John Nash (b. 1929), John Harshanyi (1920-2000) and the German economist Reinhard Selten (b. 1930). The main works of J. Nash on game theory were published in 1950-1953. The foundations of the general theory of non-cooperative games and the theory of transactions as a section of the general theory of games were laid by him in the works “Equilibrium points in games with n number of players”, 1950; "Non-cooperative games", 1951; " Co-op games with two participants”, 1953. The main contribution of J. Nash to the theory of non-cooperative games was the formulation of the concept for zero-sum games of two partners, which were previously dealt with by game theory. This concept is called the "Nash equilibrium" and has become a typical tool for studying in almost all sections of economic theory, when a comprehensive analysis of the interaction between the strategies of economic entities is needed. The Nash concept is actively used in the analysis of competition, oligopoly, the theory of industrial organization, in macroeconomics in the analysis of economic policy, protection environment. In the economics of information, J. Nash proposed a basic deal solution for games with both fixed and changing threats. Nash's work laid the foundation for the theory of cooperative and non-cooperative games as an independent theoretical discipline.

J. Harshanyi gained great fame due to the improvement of the Nash equilibrium concept for non-cooperative games with incomplete information. As a subject of analysis for this class of games, situations are taken in which economic entities not only do not reach mutual agreements, but also do not know the goals of their partners and are not informed about each other's strategy. In the series of works "Game with Incomplete Information" he developed a methodology for analyzing specific economic situations that arise in connection with decision-making in conditions of incomplete information about the position of another participant in the game. Each participant in the game was considered by Harshanyi as a player of one of the given types. He proved that for every game with incomplete information there is an equivalent game with complete information. Using the mathematical apparatus of game theory, Harshanyi transformed games with incomplete information into games with perfect information. His work laid the foundations for the information economy.

Reinhard Selten (Selten) (b. 1930) was the first to try to expand the scope of the Nash equilibrium concepts in the analysis of non-cooperative games with more than one equilibrium. His main idea was to apply stricter conditions of the game in order not only to reduce the number of possible equilibria, but also to prevent equilibria that are not economically feasible. In the work “Consideration of the oligopoly model with demand inertia in game theory”, introducing “subgame completion” into the equilibrium concept, Selten proposed a solution to this problem in the conditions of competition of several sellers. The concept of the Selten equilibrium is regarded as a fundamental improvement of the Nash equilibrium and is widely used in oligopoly analysis. In his work "Reconsideration of the completion concept for equilibrium points in extensive games", he introduced the concept of a "threatening hand" equilibrium and proposed a solution for situations in which the requirement of "subgame completion" was insufficient.

Of course, the ideas of Nash, Harshany and Selten regarding game theory and their concept of equilibria require further development. In the last 10 years, world economic thought has become increasingly interested in the behavioral and psychological determinants of social behavior, which opens up new opportunities for the development of game theory.

R. Aumann began his scientific activity in the field of applied mathematics. However, his main work is in game theory. Among the first works of Aumann there is the theory of repeated games, which is a model of the same interaction that is repeated many times. This theory helps to understand a lot of things, in particular why collaboration is difficult when there are a large number of participants or they rarely interact, when there is a high probability that the interaction will stop for exogenous reasons, when the time period is short and the behavior of opponents is considered after the break. The pattern of repeated games sheds light on the existence and functioning of various institutions, from merchant guilds to the World Trade Organization and the mafia.

The cycle of papers by R. Aumann and M. Maschler in the 1960s, devoted to repeated games with incomplete information, historically preceded the articles of 1967-1968. J. Harshanyi, who introduced the concepts of "types" of players and Bayesian equilibria in games with incomplete information.

Aumann's most important contribution to science is the concept of common knowledge, which is used in game contexts as a general characteristic of situations where players have no doubt that payoffs and sets of strategies in games with perfect information are traditionally considered common knowledge.

R. Aumann in 1965-1968 collaborated with other economists in studying the dynamics of arms control negotiations. These studies formed the basis for the theory of repeated games with incomplete information. Thus, the country does not have information about the military potential of a competitor or how it can use Additional information as an advantage.

Aumann, Shapley and Rubinstein supplemented the analysis of repeated games with complete information. In this theory, the “idea of ​​folk theory” plays a special role, the essence of which is as follows: when the interaction of participants in the same game is repeated many times, then the result of such interaction is a Pareto improvement relative to the equilibrium in a one-time game.

Aumann explored the axiomatic theory of utility without the axiom of completeness. At the same time, he proceeded from the fact that the choice sets are only partially ordered.

T. Schelling in his book "Strategy of Conflict" initiated the vision of game theory as a unified construction for the social sciences.

The second part of this book contains his earlier article, which for the first time in the economic literature formulates the concept of credible obligation to analyze the practice of self-regulation and incentive self-restraints. It is on this that R. Selten's concept of "subgame-perfect equilibrium" is based.

T. Schelling's first significant contribution to science is his behavioral analysis of bilateral trades, reflecting the essence of the conflict of interests of participants in a wide class of interactions. It is known that trade is always accompanied by conflicts of interest, since each side seeks an agreement that would bring it maximum benefit. According to Schelling, rational behavior in games consists not only in maximizing one's own income, but is also of a strategic nature, meaning that if you convince a competitor in the game that you will implement a certain strategy, then he will proceed from this given, which will limit his freedom of maneuver. . These ideas of Schelling, ahead of their time, formed the basis of the theory of strategic interaction in the second half of the 20th century.

T. Schelling put forward the problem of spatial proximity. Yes, in many major cities In the world, there are areas of compact residence of people who are similar in certain ways (Harlem in New York, where African Americans live compactly; Brighton Beach has become a kind of Russian colony; in Moscow, in the southeastern regions, the proportion of visitors from the CIS countries is high). Schelling explains this phenomenon by the fact that people in their daily lives, encountering people similar to them, gradually move to live in areas where the proportion of such people is relatively higher. Thus, the problem of sociocultural enclaves was posed by Schelling in his book Micromotives and Microbehavior.

Schelling's great merit as a scientist is to prevent a global armed conflict. In the 1950s-1960s. many military and political figures proceeded from the inevitability nuclear war. T. Schelling, together with R. Aumann and other US scientists, conducted research on American foreign policy strategy during the Cold War. The work of Schelling and his colleagues in 1962, 1974, 1976 showed that the surplus of nuclear weapons in the US and the USSR should only be a means of deterring their use.

Thomas Schelling belongs to those researchers whose works are attributed to the modernist trend in the science of international relations, primarily in such a section as the process of making a foreign policy decision. As you know, one of the common methods for studying the decision-making process is associated with game theory, which is based on probability theory and consists in constructing analysis models or predicting various types of rational behavior of interaction participants in special situations, in particular in a conflict situation.

As Russian scholars rightly noted, T. Schelling was one of the first Western researchers who realized that the zero-sum game model is not suitable for understanding an international conflict (when the gain of one participant necessarily means a loss of exactly the same scale and sides are completely opposite) 1 . Turning to more complex models of game theory, Schelling comes to the following important conclusions: the most common international conflicts are not “fixed-sum games”, but “variable-sum games”, i.e. the total gain of the participants is not fixed so that the greater gain of one of them is equivalent to exactly the same (and even comparable) loss of the other. In fact, Schelling emphasizes, the researcher must proceed from the assumption that international affairs are inherent not only in confrontation, but also in interdependence. Pure conflict, in which the interests of the two antagonists are completely opposed, is a special case; for example, this is a war of total extermination, but here we are talking no longer about the war. For this reason, "victory" in conflict is not victory over the enemy. It means winning relative to your own value system. 2 . It is with this that the second important conclusion that Schelling makes is connected. It concerns not only the gains and losses in the conflict between the two [p.251] players, but also the fact that some ways of its development or some potential ways out of the conflict, ways and results of its resolution are more (or less) preferable for both participants than others. This means that even in a situation of conflict, the interacting parties have a common interest in achieving mutually beneficial results. Thus, conflicts can be seen as situations that ultimately involve an element of pure bargaining - the conclusion of a deal in which each party is guided primarily by its own expectations of what the other is willing or able to accept. But if each of the parties proceeds from similar expectations and reasonable forecasts in relation to the other, then this means that the expectations become complementary. It follows that on the basis of mutual expectations (quite justified from the point of view of the rational behavior of the participants), a compromise between the parties to the conflict is possible.

This is the third important conclusion of Schelling, which is of particular importance in the light of the fact that every compromise presupposes and makes possible cooperation, and to a certain extent, in essence, is cooperation, although in its very initial, primitive stage.

Schelling's conclusions concerning the features of the rational behavior of the participants in the conflict became a prerequisite for the development of such a relatively independent area of ​​research in international relations as the theory of interstate cooperation. Today, the scientific community shares the position that interstate cooperation implies the presence of three elements: the common goals of the partner states, their expectation of benefits from the current situation, and the mutual nature of these benefits. 3 .

Schelling does not set the task of creating a general theory of conflict. He distinguishes two directions in the study of conflict: the first one considers the conflict as a pathological condition and searches for its causes and ways to overcome it, and the second one takes the conflict for granted and studies the behavior associated with it. Referring his work to the second direction, Schelling points out that within this direction one can single out those who explore the participants in the conflict in all their complexity - from the point of view of both "rational" and "irrational" behavior, and those who focus on rational , a conscious, deliberate form of behavior: “Roughly speaking, the last [p.252] interpret the conflict as a kind of competition in which the participants strive to "win". The study of conscious, intelligent, complex conflict behavior—successful behavior—is like finding the rules of "correct" behavior in the sense of competing to win." It is this rather narrow field of study that Schelling calls the theory of conflict, the theory of bargaining, or the theory of strategy. He writes: “...strategy, in the sense in which I use the term here, concerns the use not of actual force, but of potential force. It concerns not only enemies who hate each other, but also partners who do not trust or disagree with each other.

Schelling notes that the advantage of using the “conflict strategy” for theoretical research is not that of all possible approaches it is closest to the truth, but in the fruitfulness of the very assumption about the rational behavior of the participants in the conflict. However, in evaluating the possible application of his conclusions, he clearly goes beyond the narrow limits outlined by him. First, he believes (and, as noted above, not without certain grounds) that the strategy of conflict gives a powerful impetus to the development of the theory of international relations, bearing in mind the central role that the study of interstate clashes and confrontations plays in it. From this point of view, the methodological significance of the strategy of conflict lies in the fact that it allows us to identify our own analytical processes with the processes of hypothetical participants in the conflict; Based on the requirement of a certain sequence in relation to the hypothetical participants in the conflict, we can explore alternative types of behavior, finding out whether they meet these standards of sequence. The most important place is given to the assumption about the "rationality" of the behavior of the participants in the conflict - an assumption that plays the role of a powerful and fruitful stimulus for the development of the theory.

Secondly, Schelling sees the field of practical application of the strategy of conflict no less broad and important. In his opinion, it is applicable in almost all situations characterized by the presence of a common interest, as well as in a situation of conflict between opposite parties, such as negotiations, war and the threat of war, the fight against crime, silent bargaining, extortion, etc. “The philosophy of the book,” writes Schelling in the preface to The Strategy of Conflict, “is that it brings out the similarities in conflict strategy between, say, maneuvering in a limited war and knavery in trade, between containing the Russians and containing our own children, between the modern balance of terror and the ancient institution [p.253] hostage." Moreover, in fact, according to Schelling, any situation of interaction can ultimately be reduced to bargaining, to the expectation of benefits, extortion of concessions, maneuvering through threats and promises, boycott or intervention; in short, to a strategy of conflict. And this makes us say that for all the importance of the contribution to the study of international conflicts that was made by the works of Schelling, one cannot help but see the limited application of his conclusions to the area that he himself outlines in his book and beyond which he nevertheless goes.

It is impossible not to note one more important circumstance. Schelling's book was created and published during the period of the most acute confrontation of the Cold War era, and therefore many of its conclusions are drawn from the standpoint of the "image of the enemy", they sin with one-sidedness and bias. Moreover, in an effort to find means of "effective deterrence of the Soviet threat to the free world", its author does not stop at such recommendations for the United States as creating an effective and realistic threat of "retaliation" to the Soviet Union through the improvement of existing and the production of new types of weapons of mass destruction. 4 . But this does not negate the contribution to the study of interstate conflicts and, more broadly, to the development of the theory of international relations, which was made by Schelling's works on game models of bargaining, conflict, and strategy. The fragment of his book published below gives a certain idea of ​​the content of these models. [p.254]

Auman R., Schelling T. about game theory.

ANSWER

Nobel Prize in Economics 2005 awarded to Israeli economist R. Auman(Jerusalem University) and an American economist T. Schelling(University of Maryland) "for enriching our understanding of the nature of conflict and cooperation through the apparatus of game theory."

AUMAN Robert (b. 1930) is a well-known economist and mathematician from Frankfurt am Main (Germany). After the establishment of the fascist dictatorship, he emigrated to the United States with his parents. He received his secular and religious education in New York. In 1955 he defended his doctoral thesis in algebraic topology at the Massachusetts Institute of Technology. After working in the United States for some time in this specialty, he moved to Israel for permanent residence, where he created a school engaged in research on game theory and decision making.

SHELLING Thomas (b. 1921) is Professor Emeritus of Economics and Political Science at the University of Maryland, and Emeritus Professor of Political Economy at Harvard University, where he served for over 30 years (1959–1990) and completed his Ph.D. The beginning of the vision of game theory as a unified construction for the social sciences was laid by T. Schelling's book "Strategy of Conflict" (1960).

Auman He began his scientific activity in the field of applied mathematics. However, his main work is in game theory. One of Aumann's first works was the theory of repeated games, which is a model of the same interaction that is repeated many times. This theory helps to understand a lot of things, in particular, why collaboration is difficult when there are a large number of participants, or they rarely interact, when there is a high probability that the interaction will stop for exogenous reasons, when the time period is short and the behavior of opponents is considered after the break. The pattern of repeated games sheds light on the existence and functioning of various institutions, from merchant guilds to the World Trade Organization and the mafia.

Aumann's most important contribution to science is the concept of general knowledge, which in game contexts is used as general characteristics situations where players have no doubt that payoffs and sets of strategies in games with perfect information are traditionally considered common knowledge.

In 1965–1968 Aumann collaborated with other economists in studying the dynamics of arms control negotiations. These studies formed the basis for the theory of repeated games with incomplete information.

Schelling In his book The Strategy of Conflict, he initiated the vision of game theory as a unified framework for the social sciences.

The second part of this book contains an article that for the first time in the economic literature formulates the concept of a credible obligation to analyze the practice of self-regulation and incentive self-restraints. It is on this concept that R. Selten's concept of "subgame-perfect equilibrium" is based.

T. Schelling's first significant contribution to science is his behavioral analysis of bilateral trading, which reflects the essence of the conflict of interests of participants in a wide class of interactions. It is known that trade is always accompanied by conflicts of interest, since each side seeks an agreement that would bring it maximum benefit. According to Schelling, rational behavior in games not only consists in maximizing one's own income, but is also strategic in nature, meaning that if you convince a competitor that you will implement a certain strategy, then he will proceed from this given, which will limit his freedom of maneuver. These ideas of Schelling, ahead of their time, formed the basis of the theory of strategic interaction in the second half of the 20th century.

Schelling posed the problem of spatial proximity. So, in many large cities of the world there are areas of compact residence of people who are similar in certain ways (Harlem in New York, where African Americans live compactly; Brighton Beach, which has become a kind of Russian colony; southeastern regions of Moscow, where the share of visitors is high from CIS countries). Schelling explains this phenomenon by the fact that people, encountering similar people in everyday life, gradually move to live in areas where the proportion of such people is relatively higher. Thus, the problem of sociocultural enclaves was posed by Schelling in his book Micromotives and Microbehavior.