Abstract
The Nash theorem on the existence of equilibrium points inTV-person non-cooperative games in normal form is generalized to the case when there is a continuum of players endowed with a nonatomic measure. The mathematical tools are those used in mathematical economics, in particular, markets with a continuum of traders. The main result shows that under a restriction on the payoff functions there exists an equilibrium in pure strategies.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. J. Aumann,J. Math. Anal. Appl. 12:1–12 (1965).
K. Fan,Proc. Nat. Acad. Sci., U.S. 38:121–26 (1952).
I. Glickberg,Proc. Am. Math. Soc. 3:170–74 (1952).
J. F. Nash,Proc. Nat. Acad. Sci., U.S. 36:48–49 (1950).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Schmeidler, D. Equilibrium points of nonatomic games. J Stat Phys 7, 295–300 (1973). https://doi.org/10.1007/BF01014905
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01014905