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Schmeidler’s results on the equilibrium points of nonatomic games with strategy sets in Euclidean      n n      -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-Nikodým property. Our proofs use recent results in functional analysis.

Equilibrium points of nonatomic games over a Banach space