EQUILIBRIUM POINTS OF NONATOMIC GAMES

Schmeidler's results on the equilibrium points of nonatomic games with strategy sets in Euclidean «-space are generalized to nonatomic games with strategy sets in a Banach space. Our results also extend previous work of the author which assumed the Banach space to be separable and its dual to possess the Radon-Nikodym property. Our proofs use recent results in functional analysis.