[推荐] 本人珍藏的Nobel Lectures in Economic Sciences (1969 - 2004)

科斯说他的一生的成就大多出于偶然，这无疑是一种智者的谦虚和坦诚

John F. Nash, Jr. – Autobiography

My beginning as a legally recognized individual occurred on June 13, 1928 in Bluefield, West Virginia, in the Bluefield Sanitarium, a hospital that no longer exists. Of course I can't consciously remember anything from the first two or three years of my life after birth. (And, also, one suspects, psychologically, that the earliest memories have become "memories of memories" and are comparable to traditional folk tales passed on by tellers and listeners from generation to generation.) But facts are available when direct memory fails for many circumstances. My father, for whom I was named, was an electrical engineer and had come to Bluefield to work for the electrical utility company there which was and is the Appalachian Electric Power Company. He was a veteran of WW1 and had served in France as a lieutenant in the supply services and consequently had not been in actual front lines combat in the war. He was originally from Texas and had obtained his B.S. degree in electrical engineering from Texas Agricultural and Mechanical (Texas A. and M.). My mother, originally Margaret Virginia Martin, but called Virginia, was herself also born in Bluefield. She had studied at West Virginia University and was a school teacher before her marriage, teaching English and sometimes Latin. But my mother's later life was considerably affected by a partial loss of hearing resulting from a scarlet fever infection that came at the time when she was a student at WVU. Her parents had come as a couple to Bluefield from their original homes in western North Carolina. Her father, Dr. James Everett Martin, had prepared as a physician at the University of Maryland in Baltimore and came to Bluefield, which was then expanding rapidly in population, to start up his practice. But in his later years Dr. Martin became more of a real estate investor and left actual medical practice. I never saw my grandfather because he had died before I was born but I have good memories of my grandmother and of how she could play the piano at the old house which was located rather centrally in Bluefield. A sister, Martha, was born about two and a half years later than me on November 16, 1930. I went to the standard schools in Bluefield but also to a kindergarten before starting in the elementary school level. And my parents provided an encyclopedia, Compton's Pictured Encyclopedia, that I learned a lot from by reading it as a child. And also there were other books available from either our house or the house of the grandparents that were of educational value. Bluefield, a small city in a comparatively remote geographical location in the Appalachians, was not a community of scholars or of high technology. It was a center of businessmen, lawyers, etc. that owed its existence to the railroad and the rich nearby coal fields of West Virginia and western Virginia. So, from the intellectual viewpoint, it offered the sort of challenge that one had to learn from the world's knowledge rather than from the knowledge of the immediate community. By the time I was a student in high school I was reading the classic "Men of Mathematics" by E.T. Bell and I remember succeeding in proving the classic Fermat theorem about an integer multiplied by itself p times where p is a prime. I also did electrical and chemistry experiments at that time. At first, when asked in school to prepare an essay about my career, I prepared one about a career as an electrical engineer like my father. Later, when I actually entered Carnegie Tech. in Pittsburgh I entered as a student with the major of chemical engineering. Regarding the circumstances of my studies at Carnegie (now Carnegie Mellon U.), I was lucky to be there on a full scholarship, called the George Westinghouse Scholarship. But after one semester as a chem. eng. student I reacted negatively to the regimentation of courses such as mechanical drawing and shifted to chemistry instead. But again, after continuing in chemistry for a while I encountered difficulties with quantitative analysis where it was not a matter of how well one could think and understand or learn facts but of how well one could handle a pipette and perform a titration in the laboratory. Also the mathematics faculty were encouraging me to shift into mathematics as my major and explaining to me that it was not almost impossible to make a good career in America as a mathematician. So I shifted again and became officially a student of mathematics. And in the end I had learned and progressed so much in mathematics that they gave me an M. S. in addition to my B. S. when I graduated. I should mention that during my last year in the Bluefield schools that my parents had arranged for me to take supplementary math. courses at Bluefield College, which was then a 2-year institution operated by Southern Baptists. I didn't get official advanced standing at Carnegie because of my extra studies but I had advanced knowledge and ability and didn't need to learn much from the first math. courses at Carnegie. When I graduated I remember that I had been offered fellowships to enter as a graduate student at either Harvard or Princeton. But the Princeton fellowship was somewhat more generous since I had not actually won the Putnam competition and also Princeton seemed more interested in getting me to come there. Prof. A.W. Tucker wrote a letter to me encouraging me to come to Princeton and from the family point of view it seemed attractive that geographically Princeton was much nearer to Bluefield. Thus Princeton became the choice for my graduate study location. But while I was still at Carnegie I took one elective course in "International Economics" and as a result of that exposure to economic ideas and problems, arrived at the idea that led to the paper "The Bargaining Problem" which was later published in Econometrical. And it was this idea which in turn, when I was a graduate student at Princeton, led to my interest in the game theory studies there which had been stimulated by the work of von Neumann and Morgenstern. As a graduate student I studied mathematics fairly broadly and I was fortunate enough, besides developing the idea which led to "Non-Cooperative Games", also to make a nice discovery relating to manifolds and real algebraic varieties. So I was prepared actually for the possibility that the game theory work would not be regarded as acceptable as a thesis in the mathematics department and then that I could realize the objective of a Ph.D. thesis with the other results. But in the event the game theory ideas, which deviated somewhat from the "line" (as if of "political party lines") of von Neumann and Morgenstern's book, were accepted as a thesis for a mathematics Ph.D. and it was later, while I was an instructor at M.I.T., that I wrote up Real Algebraic Manifolds and sent it in for publication. I went to M.I.T. in the summer of 1951 as a "C.L.E. Moore Instructor". I had been an instructor at Princeton for one year after obtaining my degree in 1950. It seemed desirable more for personal and social reasons than academic ones to accept the higher-paying instructorship at M.I.T. I was on the mathematics faculty at M.I.T. from 1951 through until I resigned in the spring of 1959. During academic 1956 - 1957 I had an Alfred P. Sloan grant and chose to spend the year as a (temporary) member of the Institute for Advanced Study in Princeton. During this period of time I managed to solve a classical unsolved problem relating to differential geometry which was also of some interest in relation to the geometric questions arising in general relativity. This was the problem to prove the isometric embeddability of abstract Riemannian manifolds in flat (or "Euclidean") spaces. But this problem, although classical, was not much talked about as an outstanding problem. It was not like, for example, the 4-color conjecture. So as it happened, as soon as I heard in conversation at M.I.T. about the question of the embeddability being open I began to study it. The first break led to a curious result about the embeddability being realizable in surprisingly low-dimensional ambient spaces provided that one would accept that the embedding would have only limited smoothness. And later, with "heavy analysis", the problem was solved in terms of embeddings with a more proper degree of smoothness. While I was on my "Sloan sabbatical" at the IAS in Princeton I studied another problem involving partial differential equations which I had learned of as a problem that was unsolved beyond the case of 2 dimensions. Here, although I did succeed in solving the problem, I ran into some bad luck since, without my being sufficiently informed on what other people were doing in the area, it happened that I was working in parallel with Ennio de Giorgi of Pisa, Italy. And de Giorgi was first actually to achieve the ascent of the summit (of the figuratively described problem) at least for the particularly interesting case of "elliptic equations". It seems conceivable that if either de Giorgi or Nash had failed in the attack on this problem (of a priori estimates of Holder continuity) then that the lone climber reaching the peak would have been recognized with mathematics' Fields medal (which has traditionally been restricted to persons less than 40 years old). Now I must arrive at the time of my change from scientific rationality of thinking into the delusional thinking characteristic of persons who are psychiatrically diagnosed as "schizophrenic" or "paranoid schizophrenic". But I will not really attempt to describe this long period of time but rather avoid embarrassment by simply omitting to give the details of truly personal type. While I was on the academic sabbatical of 1956-1957 I also entered into marriage. Alicia had graduated as a physics major from M.I.T. where we had met and she had a job in the New York City area in 1956-1957. She had been born in El Salvador but came at an early age to the U.S. and she and her parents had long been U.S. citizens, her father being an M. D. and ultimately employed at a hospital operated by the federal government in Maryland. The mental disturbances originated in the early months of 1959 at a time when Alicia happened to be pregnant. And as a consequence I resigned my position as a faculty member at M.I.T. and, ultimately, after spending 50 days under "observation" at the McLean Hospital, travelled to Europe and attempted to gain status there as a refugee. I later spent times of the order of five to eight months in hospitals in New Jersey, always on an involuntary basis and always attempting a legal argument for release. And it did happen that when I had been long enough hospitalized that I would finally renounce my delusional hypotheses and revert to thinking of myself as a human of more conventional circumstances and return to mathematical research. In these interludes of, as it were, enforced rationality, I did succeed in doing some respectable mathematical research. Thus there came about the research for "Le Probleme de Cauchy pour les E'quations Differentielles d'un Fluide Generale"; the idea that Prof. Hironaka called "the Nash blowing-up transformation"; and those of "Arc Structure of Singularities" and "Analyticity of Solutions of Implicit Function Problems with Analytic Data". But after my return to the dream-like delusional hypotheses in the later 60's I became a person of delusionally influenced thinking but of relatively moderate behavior and thus tended to avoid hospitalization and the direct attention of psychiatrists. Thus further time passed. Then gradually I began to intellectually reject some of the delusionally influenced lines of thinking which had been characteristic of my orientation. This began, most recognizably, with the rejection of politically-oriented thinking as essentially a hopeless waste of intellectual effort. So at the present time I seem to be thinking rationally again in the style that is characteristic of scientists. However this is not entirely a matter of joy as if someone returned from physical disability to good physical health. One aspect of this is that rationality of thought imposes a limit on a person's concept of his relation to the cosmos. For example, a non-Zoroastrian could think of Zarathustra as simply a madman who led millions of naive followers to adopt a cult of ritual fire worship. But without his "madness" Zarathustra would necessarily have been only another of the millions or billions of human individuals who have lived and then been forgotten. Statistically, it would seem improbable that any mathematician or scientist, at the age of 66, would be able through continued research efforts, to add much to his or her previous achievements. However I am still making the effort and it is conceivable that with the gap period of about 25 years of partially deluded thinking providing a sort of vacation my situation may be atypical. Thus I have hopes of being able to achieve something of value through my current studies or with any new ideas that come in the future.

From Les Prix Nobel 1994.

John F. Nash, Jr. – Interview

Interview with Dr. John Nash by freelance journalist Marika Griehsel at the 1st Meeting of the Winners of the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel in Lindau, Germany, September 1-4, 2004. Dr. Nash talks about the impact the Prize had on his life, his talent for mathematics as a child (5:31), the work that gave him the Prize (8:55), gives some advice to young students (13:00), talks about important economic issues of today (15:20), and shares his thoughts about the movie on his life, A Beautiful Mind (21:10).

See a Video of the Interview 29 min.

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John F. Nash, Jr. – Other Resources

Links to other sites

A Brilliant Madness - The Story of Nobel Prize winning mathematician John Nash from PBS, Public Broadcasting Service

On John F. Nash from The History of Economic Thought web site

Home Page of John F. Nash, Jr. at Princeton University

Press Release: The Sveriges Riksbank (Bank of Sweden) Prize in Economic Sciences in Memory of Alfred Nobel for 1994

11 October 1994

The Royal Swedish Academy of Sciences has decided to award the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel, 1994, jointly to Professor John C. Harsanyi, University of California, Berkeley, CA, USA, Dr. John F. Nash, Princeton University, Princeton, NJ, USA, Professor Dr. Reinhard Selten, Rheinische Friedrich-Wilhelms-Universität, Bonn, Germany, for their pioneering analysis of equilibria in the theory of non-cooperative games. Games as the Foundation for Understanding Complex Economic Issues Game theory emanates from studies of games such as chess or poker. Everyone knows that in these games, players have to think ahead - devise a strategy based on expected countermoves from the other player(s). Such strategic interaction also characterizes many economic situations, and game theory has therefore proved to be very useful in economic analysis. The foundations for using game theory in economics were introduced in a monumental study by John von Neumann and Oskar Morgenstern entitled Theory of Games and Economic Behavior (1944). Today, 50 years later, game theory has become a dominant tool for analyzing economic issues. In particular, non-cooperative game theory, i.e., the branch of game theory which excludes binding agreements, has had great impact on economic research. The principal aspect of this theory is the concept of equilibrium, which is used to make predictions about the outcome of strategic interaction. John F. Nash, Reinhard Selten and John C. Harsanyi are three researchers who have made eminent contributions to this type of equilibrium analysis. John F. Nash introduced the distinction between cooperative games, in which binding agreements can be made, and non-cooperative games, where binding agreements are not feasible. Nash developed an equilibrium concept for non-cooperative games that later came to be called Nash equilibrium. Reinhard Selten was the first to refine the Nash equilibrium concept for analyzing dynamic strategic interaction. He has also applied these refined concepts to analyses of competition with only a few sellers. John C. Harsanyi showed how games of incomplete information can be analyzed, thereby providing a theoretical foundation for a lively field of research - the economics of information - which focuses on strategic situations where different agents do not know each others' objectives. Strategic Interaction Game theory is a mathematical method for analyzing strategic interaction. Many classical analyses in economics presuppose such a large number of agents that each of them can disregard the others' reactions to their own decision. In many cases, this assumption is a good description of reality, but in other cases it is misleading. When a few firms dominate a market, when countries have to make an agreement on trade policy or environmental policy, when parties on the labor market negotiate about wages, and when a government deregulates a market, privatizes companies or pursues economic policy, each agent in question has to consider other agents' reactions and expectations regarding their own decisions, i.e., strategic interaction. As far back as the early nineteenth century, beginning with Auguste Cournot in 1838, economists have developed methods for studying strategic interaction. But these methods focused on specific situations and, for a long time, no overall method existed. The game-theorethic approach now offers a general toolbox for analyzing strategic interaction. Game Theory Whereas mathematical probability theory ensued from the study of pure gambling without strategic interaction, games such as chess, cards, etc. became the basis of game theory. The latter are characterized by strategic interaction in the sense that the players are individuals who think rationally. In the early 1900s, mathematicians such as Zermelo, Borel and von Neumann had already begun to study mathematical formulations of games. It was not until the economist Oskar Morgenstern met the mathematician John von Neumann in 1939 that a plan originated to develop game theory so that it could be used in economic analysis. The most important ideas set forth by von Neumann and Morgenstern in the present context may be found in their analysis of two-person zero-sum games. In a zero-sum game, the gains of one player are equal to the losses of the other player. As early as 1928, von Neumann introduced the minimax solution for a two-person zero-sum game. According to the minimax solution, each player tries to maximize his gain in the outcome which is most disadvantageous to him (where the worst outcome is determined by his opponent's choice of strategy). By means of such a strategy, each player can guarantee himself a minimum gain. Of course, it is not certain that the players' choices of strategy will be consistent with each other. von Neumann was able to show, however, that there is always a minimax solution, i.e., a consistent solution, if so-called mixed strategies are introduced. A mixed strategy is a probability distribution of a player's available strategies, whereby a player is assumed to choose a certain "pure" strategy with some probability. John F. Nash John Nash arrived at Princeton University in 1948 as a young doctoral student in mathematics. The results of his studies are reported in his doctoral dissertation entitled Noncooperative Games (1950). The thesis gave rise to Equilibrium Points in n-person Games (Proceedings of the National Academy of Sciences of the USA 1950), and to an article entitled Non-cooperative Games, (Annals of Mathematics 1951). In his dissertation, Nash introduced the distinction between cooperative and non-cooperative games. His most important contribution to the theory of non-cooperative games was to formulate a universal solution concept with an arbitrary number of players and arbitrary preferences, i.e., not solely for two-person zero-sum games. This solution concept later came to be called Nash equilibrium. In a Nash equilibrium, all of the players' expectations are fulfilled and their chosen strategies are optimal. Nash proposed two interpretations of the equilibrium concept: one based on rationality and the other on statistical populations. According to the rationalistic interpretation, the players are perceived as rational and they have complete information about the structure of the game, including all of the players' preferences regarding possible outcomes, where this information is common knowledge. Since all players have complete information about each others' strategic alternatives and preferences, they can also compute each others' optimal choice of strategy for each set of expectations. If all of the players expect the same Nash equilibrium, then there are no incentives for anyone to change his strategy. Nash's second interpretation - in terms of statistical populations - is useful in so-called evolutionary games. This type of game has also been developed in biology in order to understand how the principles of natural selection operate in strategic interaction within and among species. Moreover, Nash showed that for every game with a finite number of players, there exists an equilibrium in mixed strategies. Many interesting economic issues, such as the analysis of oligopoly, originate in non-cooperative games. In general, firms cannot enter into binding contracts regarding restrictive trade practices because such agreements are contrary to trade legislation. Correspondingly, the interaction among a government, special interest groups and the general public concerning, for instance, the design of tax policy is regarded as a non-cooperative game. Nash equilibrium has become a standard tool in almost all areas of economic theory. The most obvious is perhaps the study of competition between firms in the theory of industrial organization. But the concept has also been used in macroeconomic theory for economic policy, environmental and resource economics, foreign trade theory, the economics of information, etc. in order to improve our understanding of complex strategic interactions. Non-cooperative game theory has also generated new research areas. For example, in combination with the theory of repeated games, non-cooperative equilibrium concepts have been used successfully to explain the development of institutions and social norms. Despite its usefulness, there are problems associated with the concept of Nash equilibrium. If a game has several Nash equilibria, the equilibrium criterion cannot be used immediately to predict the outcome of the game. This has brought about the development of so-called refinements of the Nash equilibrium concept. Another problem is that when interpreted in terms of rationality, the equilibrium concept presupposes that each player has complete information about the other players' situation. It was precisely these two problems that Selten and Harsanyi undertook to solve in their contributions. Reinhard Selten The problem of numerous non-cooperative equilibria has generated a research program aimed at eliminating "uninteresting" Nash equilibria. The principal idea has been to use stronger conditions not only to reduce the number of possible equilibria, but also to avoid equilibria which are unreasonable in economic terms. By introducing the concept of subgame perfection, Selten provided the foundation for a systematic endeavor in Spieltheoraetische Behandlung eirzes Oligopolmodelle mit Nachiragetragheit, (Zeitschrift fin die Gesamte Staatswissenschaft 121, 301-24 and 667-89, 1965). An example might help to explain this concept. Imagine a monopoly market where a potential competitor is deterred by threats of a price war. This may well be a Nash equilibrium - if the competitor takes the threat seriously, then it is optimal to stay out of the market - and the threat is of no cost to the monopolist because it is not carried out. But the threat is not credible if the monopolist faces high costs in a price war. A potential competitor who realizes this will establish himself on the market and the monopolist, confronted with fait accompli, will not start a price war. This is also a Nash equilibrium. In addition, however, it fulfills Selten's requirement of subgame perfection, which thus implies systematic formalization of the requirement that only credible threats should be taken into account. Selten's subgame perfection has direct significance in discussions of credibility in economic policy, the analysis of oligopoly, the economics of information, etc. It is the most fundamental refinement of Nash equilibrium. Nevertheless, there are situations where not even the requirement of subgame perfection is sufficient. This prompted Selten to introduce a further refinement, usually called the "trembling-hand" equilibrium, in Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games (International Journal of Game Theory 4, 25-55, 1975). The analysis assumes that each player presupposes a small probability that a mistake will occur, that someone's hand will tremble. A Nash equilibrium in a game is "trembling-hand perfect" if it is robust with respect to small probabilities of such mistakes. This and closely related concepts, such as sequential equilibrium (Kreps and Wilson, 1982), have turned out to be very fruitful in several areas, including the theory of industrial organization and macroeconomic theory for economic policy. John C. Harsanyi In games with complete information, all of the players know the other players' preferences, whereas they wholly or partially lack this knowledge in games with incomplete information. Since the rationalistic interpretation of Nash equilibrium is based on the assumption that the players know each others' preferences, no methods had been available for analyzing games with incomplete information, despite the fact that such games best reflect many strategic interactions in the real world. This situation changed radically in 1967-68 when John Harsanyi published three articles entitled Games with Incomplete Information Played by Bayesian Players, (Management Science 14, 159-82, 320-34 and 486-502). Harsanyi's approach to games with incomplete information may be viewed as the foundation for nearly all economic analysis involving information, regardless of whether it is asymmetric, completely private or public. Harsanyi postulated that every player is one of several "types", where each type corresponds to a set of possible preferences for the player and a (subjective) probability distribution over the other players' types. Every player in a game with incomplete information chooses a strategy for each of his types. Under a consistency requirement on the players' probability distributions, Harsanyi showed that for every game with incomplete information, there is an equivalent game with complete information. In the jargon of game theory, he thereby transformed games with incomplete information into games with imperfect information. Such games can be handled with standard methods. An example of a situation with incomplete information is when private firms and financial markets do not exactly know the preferences of the central bank regarding the tradeoff between inflation and unemployment. The central bank's policy for future interest rates is therefore unknown. The interactions between the forrnation of expectations and the policy of the central bank can be analyzed using the technique introduced by Harsanyi. In the most simple case, the central bank can be of two types, with adherent probabilities: Either it is oriented towards fighting inflation and thus prepared to pursue a restrictive policy with high rates, or it will try to combat unemployment by means of lower rates. Another example where similar methods can be applied is regulation of a monopoly firm. What regulatory or contractual solution will produce a desirable outcome when the regulator does not have perfect knowledge about the firm's costs? Other Contributions of the Laureates In addition to his contributions to non-cooperative game theory, John Nash has developed a basic solution for cooperative games, usually referred to as Nash's bargaining solution, which has been applied extensively in different branches of economic theory. He also initiated a project that subsequently came to be called the Nash program, a research program designed to base cooperative game theory on results from non-cooperative game theory. In addition to his prizewinning achievements, Reinhard Selten has contributed powerful new insights regarding evolutionary games and experimental game theory. John Harsanyi has also made significant contributions to the foundations of welfare economics and to the area on the boundary between economics and moral philosophy. Harsanyi and Selten have worked closely together for more than 20 years, sometimes in direct collaboration.

Through their contributions to equilibrium analysis in non-cooperative game theory, the three laureates constitute a natural combination: Nash provided the foundations for the analysis, while Selten developed it with respect to dynamics, and Harsanyi with respect to incomplete information.

The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel 1994

Presentation Speech by Professor Karl-Göran Mäler of the Royal Swedish Academy of Sciences Translation of the Swedish text

Your Majesties, Your Royal Highnesses, Ladies and Gentlemen, Many situations in society, from everyday life to high-level politics, arc characterized by what economists call strategic interactions. When there is strategic interaction, the outcome for one agent depends not only on what that agent does, but also very largely on how other agents act or react. A firm that decreases its price to attract more customers will not succeed in this strategy if the other major firms in the market use the same strategy. Whether a political party will be successful in attracting more votes by proposing lower taxes or increased spending will depend on the proposals from other parties. The success of' a central bank which is trying to fight inflation by maintaining a fixed exchange rate depends - as we know - on decisions on fiscal policy, and also on reactions in markets for labor and commodities.

A simple economic example of strategic interaction is where two firms are competing with identical products on the same market. If one firm increases its production, this will make the market price fall and therefore reduce profits for the other firm. The other firm will obviously try to counteract this, for example by increasing its production and so maintaining its market share but at the cost of further reduction in market price. The first company must therefore anticipate this countermove and possible further countermoves when it makes its decision to increase production. Can we predict how the parties will choose their strategies in situations like this?

As early as the 1830s the French economist Auguste Cournot had studied the probable outcome when two firms compete in the same market. Many economists and social scientists subsequently tried to analyze the outcome in other specific forms of strategic interaction. However, prior to the birth of game theory, there was no toolbox that gave scholars access to a general but rigorous method of analyzing different forms of strategic interaction. The situation is totally different now. Scientific journals and advanced textbooks are filled with analyses that build on game theory, as it has been developed by this year's Laureates in economics, John Nash, John Harsanyi and Reinhard Selten.

Non-cooperative game theory deals with situations where the parties cannot make binding agreements. Even in very complicated games, with many parties and many available strategies, it will be possible to describe the outcome in terms of a so-called Nash equilibrium - so named after one of the Laureates. John Nash has shown that there is at least one stable outcome, that is an outcome such that no player can improve his own outcome by choosing a different strategy when all players have correct expectations of each other's strategy. Even if each party acts in an individually rational way, the Nash equilibrium shows that strategic interaction can quite often cause collective irrationality: trade wars or excessive emission of pollutants that threaten the global environment are examples in the international sphere. One should also add that the Nash equilibrium has been important within evolutionary ecology - to describe natural selection as a strategic interaction within and between species.

In many games, the players lack complete information about each other's objective. If the government, for example, wants to deregulate a firm but does not know the cost situation in the firm, while the firm's management has this knowledge, we have a game with incomplete information. In three articles published toward the end of the 1960s, John Harsanyi showed how equilibrium analysis could be extended to handle this difficulty, which game theorists up to that time had regarded as insurmountable. Harsanyi's approach has laid an analytical basis for several lively research areas including information economics which starts from the fact that different decision makers, in a market or within an organization, often have access to different information. These areas cover a broad range of issues, from contracts between shareholders and a company's management to institutions in developing countries.

One problem connected with the concept of Nash equilibrium is that there may be several equilibria in non-cooperative games. It may thus be difficult - both for the players and an outside analyst - to predict the outcome. Reinhard Selten has, through his "perfection" concepts, laid the foundations for the research program that has tried to exclude improbable or unreasonable equilibria. Certain Nash equilibria can, in fact, be such that they are based on threats or promises intended to make other players choose certain strategies. These threats and promises are often empty because it is not in the player's interest to carry them out if a situation arises in which he has threatened to carry them out. By excluding such empty threats and promises Selten could make stronger predictions about the outcome in the form of socalled perfect equilibria.

Selten's contributions have had great importance for analysis of the dynamics of strategic interaction, for example between firms trying to reach dominant positions on the market, or between private agents and a government that tries to implement a particular economic policy.

Professor John Harsanyi, the analysis of games with incomplete information is due to you, and it has been of great importance for the economics of information.

Dr John Nash, your analysis of equilibria in non-cooperative games, and all your other contributions to game theory, have had a profound effect on the way economic theory has developed in the last two decades. Professor Reinhard Selten, your notion of perfection in the equilibrium analysis has substantially extended the use of non-cooperative game theory.

It is an honour and a privilege for me to convey to all of you, on behalf of the Royal Swedish Academy of Sciences, our warmest congratulations. I now ask you to receive your prizes from the hands of his Majesty the King.

From Nobel Lectures, Economics 1991-1995, Editor Torsten Persson, World Scientific Publishing Co., Singapore, 1997

Game Theory Explained

Avinash Dixit, John J. F. Sherrerd '52 University Professor of Economics at Princeton University, is John Nash's colleague and friend. He has taught economics courses on games of strategy, and written books on the subject for students and for the general audience.

Here Prof. Dixit explains game theory and its impact on situations we encounter every day. "If Nash got a dollar for every time someone wrote or said 'Nash equilibrium,'" Dixit has said, "he would be a rich man."

Game theory studies interactive decision-making, where the outcome for each participant or "player" depends on the actions of all. If you are a player in such a game, when choosing your course of action or "strategy" you must take into account the choices of others. But in thinking about their choices, you must recognize that they are thinking about yours, and in turn trying to take into account your thinking about their thinking, and so on.

It would seem that such thinking about thinking must be so complex and subtle that its successful practice must remain an arcane art. Indeed, some aspects such as figuring out the true motives of rivals and recognizing complex patterns do often resist logical analysis. But many aspects of strategy can be studied and systematized into a science -- game theory.

A Theory is Born This science is unusual in the breadth of its potential applications. Unlike physics or chemistry, which have a clearly defined and narrow scope, the precepts of game theory are useful in a whole range of activities, from everyday social interactions and sports to business and economics, politics, law, diplomacy and war. Biologists have recognized that the Darwinian struggle for survival involves strategic interactions, and modern evolutionary theory has close links with game theory.

Game theory got its start with the work of John von Neumann in the 1920s, which culminated in his book with Oskar Morgenstern. They studied "zero-sum" games where the interests of two players were strictly opposed. John Nash treated the more general and realistic case of a mixture of common interests and rivalry and any number of players. Other theorists, most notably Reinhard Selten and John Harsanyi who shared the 1994 Nobel Memorial Prize with Nash, studied even more complex games with sequences of moves, and games where one player has more information than others.

The Nash Equilibrium The theory constructs a notion of "equilibrium," to which the complex chain of thinking about thinking could converge. Then the strategies of all players would be mutually consistent in the sense that each would be choosing his or her best response to the choices of the others. For such a theory to be useful, the equilibrium it posits should exist. Nash used novel mathematical techniques to prove the existence of equilibrium in a very general class of games. This paved the way for applications. Biologists have even used the notion of Nash equilibrium to formulate the idea of evolutionary stability. Here are a few examples to convey some ideas of game theory and the breadth of its scope.

The Prisoner's Dilemma In Joseph Heller's novel Catch-22, allied victory in World War II is a foregone conclusion, and Yossarian does not want to be among the last ones to die. His commanding officer points out, "But suppose everyone on our side felt that way?" Yossarian replies, "Then I'd certainly be a damned fool to feel any other way, wouldn't I?"

Every general reader has heard of the prisoner's dilemma. The police interrogate two suspects separately, and suggest to each that he or she should fink on the other and turn state's evidence. "If the other does not fink, then you can cut a good deal for yourself by giving evidence against the other; if the other finks and you hold out, the court will treat you especially harshly. Thus no matter what the other does, it is better for you to fink than not to fink -- finking is your uniformly best or 'dominant' strategy." This is the case whether the two are actually guilty, as in some episodes of NYPD Blue, or innocent, as in the film LA Confidential. Of course, when both fink, they both fare worse than they would have if both had held out; but that outcome, though jointly desirable for them, collapses in the face of their separate temptations to fink.

Yossarian's dilemma is just a multi-person version of this. His death is not going to make any significant difference to the prospects of victory, and he is personally better off alive than dead. So avoiding death is his dominant strategy.

John Nash played an important role in interpreting the first experimental study of the prisoner's dilemma, which was conducted at the Rand Corporation in 1950.

Real-World Dilemmas Once you recognize the general idea, you will see such dilemmas everywhere. Competing stores who undercut each other's prices when both would have done better if both had kept their prices high are victims of the dilemma. (But in this instance, consumers benefit from the lower prices when the sellers fink on each other.) The same concept explains why it is difficult to raise voluntary contributions, or to get people to volunteer enough time, for worthwhile public causes.

How might such dilemmas be resolved? If the relationship of the players is repeated over a long time horizon, then the prospect of future cooperation may keep them from finking; this is the well-known tit-for-tat strategy. A "large" player who suffers disproportionately more from complete finking may act cooperatively even when the small fry are finking. Thus Saudi Arabia acts as a swing producer in OPEC, cutting its output to keep prices high when others produce more; and the United States bears a disproportionate share of the costs of its military alliances. Finally, if the group as a whole will do better in its external relations if it enjoys internal cooperation, then the process of biological or social selection may generate instincts or social norms that support cooperation and punish cheating. The innate sense of fairness and justice that is observed among human subjects in many laboratory experiments on game theory may have such an origin.

Mixing Moves In football, when an offense faces a third down with a yard to go, a run up the middle is the usual or "percentage" play. But an occasional long pass in such a situation is important to keep the defense honest. Similarly, a penalty kicker in soccer who kicks exclusively to the goalie's right, or a server in tennis who goes exclusively to the receiver's forehand, will fare poorly because the opponent will anticipate and counter the action. In such situations it is essential to mix one's moves randomly, so that on any one occasion the action is unpredictable.

Mixing is most important in games where the players' interests are strictly opposed, and this happens most frequently in sports. Indeed, recent empirical studies of serving in tennis grand slam finals, and penalty kicks in European soccer leagues, have found the behavior consistent with the theory.

Commitments Greater freedom of action seems obviously desirable. But in games of bargaining that need not be true, because freedom to act can simply become freedom to concede to the other's demands. Committing yourself to a firm final offer leaves the other party the last chance to avoid a mutually disastrous breakdown, and this can get you a better deal. But a mere verbal declaration of firmness may not be credible. Devising actions to make one's commitments credible is one of the finer arts in the realm of strategic games. Members of a labor union send their leaders into wage bargaining with firm instructions or mandates that tie their hands, thereby making it credible that they will not accept a lower offer. The executive branch of the U.S. government engaged in international negotiations on trade or related matters can credibly take a firm stance by pointing out that the Congress would not ratify anything less. And a child is more likely to get the sweet or toy it wants if it is crying too loudly to hear your reasoned explanations of why it should not have it.

Thomas Schelling pioneered the study of credible commitments, and other more complex "strategic moves" like threats and promises. This has found many applications in diplomacy and war, which, as military strategist Karl von Clausewitz told us long ago, are two sides of the same strategic coin.

Information and Incentives Suppose you have just graduated with a major in computer science, and have an idea for a totally new "killer app" that will integrate PCs, cell phones, and TV sets to create a new medium. The profit potential is immense. You go to venture capitalists for finance to develop and market your idea. How do they know that the potential is as high as you claim it to be? The idea is too new for them to judge it independently. You have no track record, and might be a complete charlatan who will use the money to live high for a few years and then disappear. One way for them to test your own belief in your idea is to see how much of your own money you are willing to risk in the project. Anyone can talk a good game; if you are willing to put enough of your money where your mouth is, that is a credible signal of your own true valuation of your idea.

This is a game where the players have different information; you know the true potential of your idea much better than does your prospective financier. In such games, actions that reveal or conceal information play crucial roles. The field of "information economics" has clarified many previously puzzling features of corporate governance and industrial organization, and has proved equally useful in political science, studies of contract and tort law, and even biology. The award of the Nobel Memorial Prize in 2001 to its pioneers, George Akerlof, Michael Spence, and Joseph Stiglitz, testifies to its importance. What has enabled information economics to burgeon in the last twenty years is the parallel development of concepts and techniques in game theory.

Aligning Interests, Avoiding Enrons A related application in business economics is the design of incentive schemes. Modern corporations are owned by numerous shareholders, who do not personally supervise the operations of the companies. How can they make sure that the workers and managers will make the appropriate efforts to maximize shareholder value? They can hire supervisors to watch over workers, and managers to watch over supervisors. But all such monitoring is imperfect: the time on the job is easily monitored, but the quality of effort is very difficult to observe and judge. And there remains the problem of who will watch over the upper-level management. Hence the importance of compensation schemes that align the interests of the workers and managers with those of the shareholders. Game theory and information economics have given us valuable insights into these issues. Of course we do not have perfect solutions; for example, we are just discovering how top management can manipulate and distort the performance measures to increase their own compensation while hurting shareholders and workers alike. This is a game where shareholders and the government need to find and use better counterstrategies.

From Intuition to Prediction While reading these examples, you probably thought that many of the lessons of game theory are obvious. If you have had some experience of playing similar games, you have probably intuited good strategies for them. What game theory does is to unify and systematize such intuitions. Then the general principles extend the intuitions across many related situations, and the calculation of good strategies for new games is simplified. It is no bad thing if an idea seems obvious when it is properly formulated and explained; on the contrary, a science or theory that takes simple ideas and brings out their full power and scope is all the more valuable for that.

In conclusion, I offer some suggestions for further reading to those whose appetites are whetted by my sampler of examples. (This site's bibliography includes some Web sites of interest.)

General interest: Dixit, Avinash, and Barry Nalebuff. Thinking Strategically: the Competitive Edge in Business, Politics, and Everyday Life. New York: W.W. Norton, 1991.

Schelling, Thomas. The Strategy of Conflict. Revised edition. Cambridge: Harvard University Press, 1980.

Elementary textbook: Dixit, Avinash, and Susan Skeath. Games of Strategy. New York: W.W. Norton, 1999.

Advanced textbooks: Fudenberg, Drew, and Jean Tirole. Game Theory. Cambridge, Massachusetts: MIT Press, 1991.

Myerson, Roger . Game Theory: Analysis of Conflict. Cambridge, Massachusetts: Harvard University Press, 1991.

Business applications: Brandenberger, Adam, and Barry Nalebuff. Co-opetition. New York: Doubleday, 1996.

McMillan, John. Games, Strategies, and Managers. Reprint. New York: Oxford University Press, 1996.

Political science applications: Brams, Steven. Rational Politics: Decisions, Games, and Strategy. Reprint. Boston: Academic Press, 1989.

Ordeshook, Peter, A Political Theory Primer. New York: Routledge, 1992.

Applications to law: Baird, Douglas, Gertner, Robert, and Randal Picker. Game Theory and the Law. Cambridge, Massachusetts: Harvard University Press, 1994.

Biology: Maynard Smith, John. Evolution and the Theory of Games. Cambridge, England: Cambridge University Press, 1982.

Classic books about game theory: Luce, R. Duncan, and Howard Raiffa. Games and Decisions: Introduction and Critical Survey. New York: Wiley, 1957.

von Neumann, John, and Oskar Morgenstern. Theory of Games and Economic Behavior. Second edition. Princeton, New Jersey: Princeton University Press, 1947.

Interview with John Nash

According to Aristotle, the best tragedies are conflicts between a hero and his destiny. They contain reversals of fortune, moments of recognition, and, ultimately, a catharsis. Dr. John Nash's life -- his early brilliance, his struggle with mental illness, and his slow, willful recovery -- is definitely the stuff of Greek tragedy. He describes his experiences, in these excerpts from an in-depth interview.

Discovering Math The Most Original Non-Conformity Alicia The Downward Spiral Hearing Voices Misconceptions about Mental Illness My Experience with Mental Illness Being Institutionalized Insulin Coma Therapy Medication Delusional Thinking Paths Toward Recovery How Does Recovery Happen? The Nobel Prize -- and the Future

The Colored Words can direct you to another wonderful place！ Plz try them

More about the film A Brilliant Madness

A Brilliant Madness is the story of a mathematical genius whose career was cut short by a descent into madness. At the age of 30, John Nash, a stunningly original and famously eccentric MIT mathematician, suddenly began claiming that aliens were communicating with him and that he was a special messenger. Diagnosed with paranoid schizophrenia, Nash spent the next three decades in and out of mental hospitals, all but forgotten. During that time, a proof he had written at the age of 20 became a foundation of modern economic theory. In 1994, as Nash began to show signs of emerging from his delusions, he was awarded a Nobel Prize in Economics. The program features interviews with John Nash, his wife Alicia, his friends and colleagues, and experts in game theory and mental illness.

Film Description A synopsis of the film, plus film credits.

Transcript The program transcript.

Primary Sources John Nash's dissertation, his Nobel autobiography... and information on insulin coma therapy.

Further Reading A list of books, articles, and Web sites relating to the program topic.

Acknowledgements Program interviewees and consultants.

	AMERICAN EXPERIENCE is closed captioned for deaf and hard-of-hearing viewers by The Caption Center at WGBH.
	A special narration track is added to the series by Descriptive Video Service® (DVS®), a service of WGBH to provide access to people who are blind or visually impaired. The DVS narration is available on the SAP channel of stereo TVs and VCRs.

Film Description

The life of the Nobel Prize-winning mathematician and schizophrenic John Nash -- the inspiration for the feature film A Beautiful Mind- -- is a powerful exploration of how genius and madness can become intertwined.

Hailed as a mathematical genius and one of the most original minds of the 20th century, Nash made his breakthrough as a twenty-year-old graduate student at Princeton with a stunning proof in the field of game theory. His thesis of the dynamics of human conflict would revolutionize economics, and would eventually win him the Nobel Prize.

But at the height of his career, after a decade of remarkable mathematical accomplishments, Nash suffered a breakdown. The 30-year-old MIT professor interrupted a lecture to announce he was on the cover of Life magazine -- disguised as the pope. He claimed that foreign governments were communicating with him through The New York Times, and turned down a prestigious post at the University of Chicago because, he said, he was about to become the Emperor of Antarctica.

His wife Alicia had him committed against his will to a private mental hospital, where he was diagnosed with paranoid schizophrenia and treated with psychoanalysis. Upon his release, Nash abruptly resigned from MIT, withdrew his pension fund and fled to Europe. He wandered from country to country, attempting to renounce his American citizenship and be declared a refugee. He saw himself as a secret messenger of God and the focus of an international communist conspiracy. With help from the State Department, Alicia had him deported back to the U.S.

Desperate and short of funds, Alicia was forced to commit her husband to the former New Jersey Lunatic Asylum, an understaffed state institution. There Nash was subjected to insulin coma therapy, an aggressive and life-threatening treatment. When he was released after six months, "he looked like he had been battered and been through some devastating thing," recalls a friend. "It was heartbreaking." Mathematicians were outraged; no one knew what the impact of treatment on Nash's genius would be.

John and Alicia were soon divorced. His former colleagues tried to help him through his illness, on several occasions securing him jobs during his remissions, but each time his delusions would return and he'd be forced to give up work. After a number of additional stints in hospitals, Alicia let him move back in with her, vowing to never commit him again. Throughout the 1960s, he wandered the campus of his alma mater in red high-top sneakers, keeping to himself; students teased him and called him the Phantom.

Beginning in the 1980s, Nash experienced his second inexplicable transformation: gradually, his schizophrenia began to taper off. "I began arguing with the concept of the voices," he recalls. "And ultimately I began rejecting them and deciding not to listen."

During the period of his recovery, game theory became a foundation of modern economic theory and Nash began to be considered for a Nobel Prize in Economics. Nobel committee members balked, afraid Nash would prove an embarrassment. But his supporters finally won. In 1994 Nash received his award, capping his dramatic reawakening from madness.

The producers of A Brilliant Madness gained unprecedented access to the Nash family to tell this story. The film features interviews with Nash, his sister, his oldest son, close friends and colleagues as well as many family photographs. In addition to archival materials, the film uses a range of film stocks and cinematic techniques to vividly recreate Nash's foggy world of paranoid delusions. Yet, the star of the film is undoubtedly Nash himself. He is disarmingly honest about his work, his ambitions and his illness. "Madness can be an escape," he says. "If things are not so good, you maybe want to imagine something better. In madness, I thought I was the most important person of the world."

Film Credits