The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Nash Equilibrium

  • David M. Kreps
Reference work entry


The concept of a Nash equilibrium plays a central role in noncooperative game theory. Due in its current formalization to John Nash (1950, 1951), it goes back at least to Cournot (1838). This entry begins with the formal definition of a Nash equilibrium and with some of the mathematical properties of equilibria. Then we ask: To what question is ‘Nash equilibrium’ the answer? The answer that we suggest motivates further questions of equilibrium selection, which we consider in two veins: the informal notions, such as Schelling’s (1960) focal points; and the formal theories for refining or perfecting Nash equilibria, due largely to Selten (1965, 1975). We conclude with a brief discussion of two related issues: Harsanyi’s (1967–8) notion of a game of incomplete information and Aumann’s (1973) correlated equilibria.

This is a preview of subscription content, log in to check access.


  1. Aumann, R. 1973. Subjectivity and correlation in randomized strategies. Journal of Mathematical Economics 1: 67–96.CrossRefGoogle Scholar
  2. Aumann, R. 1987. Correlated equilibrium as an expression of Bayesian rationality. Econometrica 55: 1–18.CrossRefGoogle Scholar
  3. Bernheim, D. 1984. Rationalizable strategic behavior. Econometrica 52: 1007–1028.CrossRefGoogle Scholar
  4. Cournot, A. 1838. Recherches sur les principes mathématiques de la théorie des richesses. Paris. Trans. as Researches into the mathematical principles of the theory of wealth. New York: Macmillan and Company, 1897.Google Scholar
  5. Farrell, J. 1985. Communication equilibria in games. Waltham: GTE Laboratories.Google Scholar
  6. Forges, F. 1986. An approach to communication equilibrium. Econometrica 54(6): 1375–1385.CrossRefGoogle Scholar
  7. Harsanyi, J. 1967–8. Games with incomplete information played by Bayesian players. Parts I, II, and III. Management Science 14: 159–82, 320–334. 486–502.Google Scholar
  8. Harsanyi, J. 1975. The tracing procedure. International Journal of Game Theory 4: 61–94.CrossRefGoogle Scholar
  9. Kohlberg, E., and J.-F. Mertens. 1982. On the strategic stability of equilibrium. Working paper, CORE, Catholic University of Louvain, forthcoming in Econometrica.Google Scholar
  10. Kreps, D., and R. Wilson. 1982. Sequential equilibrium. Econometrica 50: 863–894.CrossRefGoogle Scholar
  11. Kuhn, H. 1953. Extensive games and the problem of information. In Contributions to the theory of games, vol. 2, ed. H. Kuhn and A. Tucker. Princeton: Princeton University Press.Google Scholar
  12. Luce, D.R., and H. Raiffa. 1957. Games and decisions. New York: Wiley.Google Scholar
  13. Myerson, R. 1978. Refinements of the Nash equilibrium concept. International Journal of Game Theory 7: 73–80.CrossRefGoogle Scholar
  14. Myerson, R. 1984. Sequential equilibria of multistage games. DMSEMS discussion paper no. 590, Northwestern University.Google Scholar
  15. Nash, J.F. 1950. Equilibrium points in n-person games. Proceedings of the National Academy of Sciences USA 36: 48–49.CrossRefGoogle Scholar
  16. Nash, J.F. 1951. Non-cooperative games. Annals of Mathematics 54: 286–295.CrossRefGoogle Scholar
  17. Pearce, D. 1984. Rationalizable strategic behavior and the problem of perfection. Econometrica 52: 1029–1050.CrossRefGoogle Scholar
  18. Roth, A., and F. Schoumaker. 1983. Expectations and reputations in bargaining: An experimental study. American Economic Review 73: 362–372.Google Scholar
  19. Rubinstein, A. 1982. Perfect equilibrium in a bargaining model. Econometrica 50: 97–109.CrossRefGoogle Scholar
  20. Schelling, T. 1960. The strategy of conflict. Cambridge, MA: Harvard University Press.Google Scholar
  21. Selten, R. 1965. Spieltheoretische Behandlung eines Oligopolmodells mit Nachfragetragheit. Zeitschrift für die gesamte Staatswissenschaft 121: 301–324.Google Scholar
  22. Selten, R. 1975. Re-examination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory 4: 25–55.CrossRefGoogle Scholar
  23. Selten, R. 1978. The chain-store paradox. Theory and Decision 9: 127–159.CrossRefGoogle Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • David M. Kreps
    • 1
  1. 1.