, Volume 7, Issue 4, pp 295-300

Equilibrium points of nonatomic games

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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.

An earlier version of this paper was presented at the Third Annual Israeli Conference on Operations Research, 1969. This version was prepared in the Center for Operations Research and Econometrics, Université Catholique de Louvain, and reviewed in Tel-Aviv University.