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Journal of Statistical Physics

, Volume 7, Issue 4, pp 295–300 | Cite as

Equilibrium points of nonatomic games

  • David Schmeidler
Articles

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.

Key words

Games nonatomic games equilibrium point set-valued function fixed point 

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References

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    R. J. Aumann,J. Math. Anal. Appl. 12:1–12 (1965).Google Scholar
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    K. Fan,Proc. Nat. Acad. Sci., U.S. 38:121–26 (1952).Google Scholar
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    I. Glickberg,Proc. Am. Math. Soc. 3:170–74 (1952).Google Scholar
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    J. F. Nash,Proc. Nat. Acad. Sci., U.S. 36:48–49 (1950).Google Scholar

Copyright information

© Plenum Publishing Corporation 1973

Authors and Affiliations

  • David Schmeidler
    • 1
  1. 1.Department of EconomicsTel-Aviv UniversityTel-AvivIsrael

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