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Article

On Maximal Vector Spaces of Finite Noncooperative Games

International Game Theory Review. 2017. Vol. 19. No. 2.

We consider finite noncooperative (Formula presented.) person games with fixed numbers (Formula presented.), (Formula presented.), of pure strategies of Player (Formula presented.). We propose the following question: is it possible to extend the vector space of finite noncooperative (Formula presented.)-games in mixed strategies such that all games of a broader vector space of noncooperative (Formula presented.) person games on the product of unit (Formula presented.)-dimensional simplices have Nash equilibrium points? We get a necessary and sufficient condition for the negative answer. This condition consists of a relation between the numbers of pure strategies of the players. For two-person games the condition is that the numbers of pure strategies of the both players are equal.