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=(Xi;Ti,fi), we prove a mixed equilibrium existence theorem for the generalized mixed strategic game Gˆ=(Δ(Xi);Tˆi,fˆi) without assuming the convexity of strategy space Xi. Finally, two examples of the Nash equilibrium and mixed equilibrium for generalized strategic games G=(Xi;Ti,fi) are given.