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On Maximal Vector Spaces of Finite Non-Cooperative Games

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  • Victoria Kreps

    (National Research University Higher School of Economics)

Abstract

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

Suggested Citation

  • Victoria Kreps, 2016. "On Maximal Vector Spaces of Finite Non-Cooperative Games," HSE Working papers WP BRP 150/EC/2016, National Research University Higher School of Economics.
    • Handle: RePEc:hig:wpaper:150/ec/2016
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    Keywords

    Finite non-cooperative N person games; vector space; Nash equilibrium point; maximality.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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