Abstract
Nash equilibrium is the central notion of rational behaviour in non-cooperative game theory (see Osborne and Rubinstein, 1994, for a discussion of Nash equilibrium, including motivation and interpretation). Our purpose here is to discuss various conditions under which a strategic form game possesses at least one Nash equilibrium.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliography
Baye, M., Tian, G. and Zhou, J. 1993. Characterizations of the existence of equilibria in games with discontinuous and non-quasiconcave payoffs. Review of Economic Studies 60, 935–48.
Bertrand, J. 1883. Théorie mathématique de la richesse sociale. Journal des Savants 67, 499–508.
Billingsley, P. 1968. Convergence of Probability Measures. New York: John Wiley and Sons.
Cournot, A. 1838. Researches into the Mathematical Principles of the Theory of Wealth, ed. N. Bacon. New York: Macmillan, 1897.
Dasgupta, P. and Maskin, E. 1986. The existence of equilibrium in discontinuous economic games, I: theory. Review of Economic Studies 53, 1–26.
Debreu, G. 1952. A social equilibrium existence theorem. Proceedings of the National Academy of Sciences 38, 386–93.
Fudenberg, D., Gilbert, R., Stiglitz, J. and Tirole, J. 1983. Preemption, leapfrogging, and competition in patent races. European Economic Review 22, 3–31.
Glicksberg, I. 1952. A further generalization of the Kakutani fixed point theorem. Proceedings of the American Mathematical Society 3, 170–4.
Hotelling, H. 1929. The stability of competition. Economic Journal 39, 41–57.
Jackson, M. and Swinkels, J. 2005. Existence of equilibrium in single and double private value auctions. Econometrica 73, 93–139.
Jackson, M., Simon, L., Swinkels, J. and Zame, W. 2002. Communication and equilibrium in discontinuous games of incomplete information. Econometrica 70, 1711–40.
Milgrom, P. and Roberts, J. 1990. Rationalizability learning, and equilibrium in games with strategic complementarities. Econometrica 58, 1255–77.
Milgrom, P. and Weber, R. 1982. A theory of auctions and competitive bidding. Econometrica 50, 1089–122.
Milgrom, P. and Weber, R. 1985. Distributional strategies for games with incomplete information. Mathematics of Operations Research 10, 619–32.
Nash, J. 1950. Equilibrium points in n-person games. Proceedings of the National Academy of Sciences 36, 48–9.
Nash, J. 1951. Non-cooperative games. Annals of Mathematics 54, 286–95.
Osborne, M. and Rubinstein, A. 1994. A Course in Game Theory. Cambridge, MA: MIT Press.
Reny P. 1999. On the existence of pure and mixed strategy Nash equilibria in discontinuous games. Econometrica 67, 1029–56.
Robson, A. 1994. An ‘informationally robust’ equilibrium in two-person nonzero-sum games. Games and Economic Behavior 2, 233–45.
Schäfer, W. and Sonnenschein, H. 1975. Equilibrium in Abstract economies without ordered preferences. Journal of Mathematical Economics 2, 345–8.
Simon, L. 1987. Games with discontinuous payoffs. Review of Economic Studies 54, 569–97.
Simon, L. and Zame, W. 1990. Discontinuous games and endogenous sharing rules. Econometrica 58, 861–72.
Sion, M. 1958. On general minimax theorems. Pacific Journal of Mathematics 8, 171–6.
Vives, X. 1990. Nash equilibrium with strategic complementarities. Journal of Mathematical Economics 19, 305–21.
von Neumann, J. 1928. Zur Theorie der Gesellshaftspiele. Mathematische Annalen 100, 295–320. Trans. S. Bargmann [On the theory of games of strategy] in Contributions to the Theory of Games, vol. 4, ed. R. Luce and A. Tucker. Princeton: Princeton University Press, 1959.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Copyright information
© 2010 Palgrave Macmillan, a division of Macmillan Publishers Limited
About this chapter
Cite this chapter
Durlauf, S.N., Blume, L.E. (2010). Non-Cooperative Games (Equilibrium Existence). In: Durlauf, S.N., Blume, L.E. (eds) Game Theory. The New Palgrave Economics Collection. Palgrave Macmillan, London. https://doi.org/10.1057/9780230280847_27
Download citation
DOI: https://doi.org/10.1057/9780230280847_27
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-0-230-23890-9
Online ISBN: 978-0-230-28084-7
eBook Packages: Palgrave Media & Culture CollectionLiterature, Cultural and Media Studies (R0)