Existence of a mixed equilibrium for a compact generalized strategic game

In this paper, we first introduce new concepts of generalized mixed strategic game and mixed equilibrium which generalize the mixed equilibrium for a compact strategic game due to Nash. Next, by using an equilibrium existence theorem for the compact convex strategic game G = ( X i ; T i , f i ) , we prove a mixed equilibrium existence theorem for the generalized mixed strategic game G ˆ = ( Δ ( X i ) ; T ˆ i , f ˆ i ) without assuming the convexity of strategy space X i . Finally, two examples of the Nash equilibrium and mixed equilibrium for generalized strategic games G = ( X i ; T i , f i ) are given.