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.
Gamesnonatomic gamesequilibrium pointset-valued functionfixed point