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On Maximal Vector Spaces of Finite Non-Cooperative Games
NRU Higher School of Economics
,
2016.
No. WP BRP 150/EC/2016.
Kreps V. L.
We consider finite non-cooperative N person games with fixed numbers mi, i = 1, . . . , N , of pure strategies of player i. We propose the following question: is it possible to extend the vector space of finite non-cooperative m1 × m2 × . . . × mN - games in mixed strategies such that all games of a broader vector space of non- cooperative N person games on the product of unit (mi − 1)-dimensional simpleces 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
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