Journal of Statistical Physics

, Volume 7, Issue 4, pp 295–300

Equilibrium points of nonatomic games

  • David Schmeidler

DOI: 10.1007/BF01014905

Cite this article as:
Schmeidler, D. J Stat Phys (1973) 7: 295. doi:10.1007/BF01014905


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

Gamesnonatomic gamesequilibrium pointset-valued functionfixed point

Copyright information

© Plenum Publishing Corporation 1973

Authors and Affiliations

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