Nash equilibrium and the history of economic theory

NASH EQUILIBRIUM AND THE HISTORY OF ECONOMIC THEORY by Roger B. Myerson

first version, April 1996 revised, March 1999

Abstract. John Nash's formulation of noncooperative game theory was one of the great breakthroughs in the history of social science. Nash's work in this area is reviewed in its historical context, to better understand how the fundamental ideas of noncooperative game theorywere developed and how they changed the course of economic theory. JEL Classification numbers: B20, C72

Author's address: Department of Economics, University of Chicago, 1126 E 59th Street, Chicago, IL 606037. E-mail: myerson@uchicago.edu URL: http://home.uchicago.edu/~rmyerson/ This paper is published in the Journal of Economic Literature 36:1067-1082 (1999), which is the only definitiverepository of the content that has been certified and accepted after peer review.

NASH EQUILIBRIUM AND THE HISTORY OF ECONOMIC THEORY by Roger B. Myerson, Northwestern University

1. Looking back on an intellectual revolution November 16, 1999 marks the fiftieth anniversary of the day that John Nash's first paper on noncooperative equilibrium was received by the editorial offices of theProceedings of the National Academy of Sciences. The fiftieth anniversary of a major event can be a good time to look back at it, when we are still linked to it by living memories, but we have enough distance to see some of its broader historical significance. From this perspective, Nash's theory of noncooperative games should now be recognized as one of the outstanding intellectual advances of thetwentieth century. The formulation of Nash equilibrium has had a fundamental and pervasive impact in economics and the social sciences which is comparable to that of the discovery of the DNA double helix in the biological sciences. Yet even now, there are still current books on the history of economic thought that fail to allocate even one full page to Nash's work (see Niehans, 1990), and prominentscholars can search for a "consilient" unification of social science with virtually no regard for the real unification that has been provided by noncooperative game theory (see Wilson, 1998). So it is appropriate that we should now re-examine Nash's work in its broader historical context, to see how a few short papers by a young mathematician achieved one of the great watershed breakthroughs in thehistory of social science. Weintraub (1992) offers a good overview of the early history of game theory, with a particular focus on the work of von Neumann and Morgenstern (see also Morgenstern, 1976). 1

Since 1994, when the Nobel Memorial Prize in Economic Sciences was awarded to John Nash, John Harsanyi, and Reinhard Selten, there have been a number of essays in appreciation of Nash's work; seeLeonard (1994), Kuhn (1994), Milnor (1995), Rubinstein (1995), van Damme and Weibull (1995), Myerson (1996), and Binmore's introduction to the collected game-theory papers of Nash (1996). A detailed biography of John Nash has been written by Sylvia Nasar (1998). In this paper, to show how Nash's work was a major turning-point in the history of economic thought, we try to place his contributions intheir broader historical context. So in addition to reviewing Nash's most important contributions, we also examine some of Nash's precursors and followers. Our goal is to better appreciate how economic theory was transformed by Nash's ideas, and to understand why these ideas were developed at his point in time and were not seen earlier. To understand both the importance of Nash's work and how itcould be overlooked in histories of economic thought, we should begin with the very definition of economics itself. A generation before Nash could have accepted a narrower definition of economics, as a specialized social science concerned with the production and allocation of material goods. With this narrower definition, Nash's work could be seen at first as mathematical research near the...