On Maximal Vector Spaces of Finite Noncooperative Games

Victoria Kreps
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Victoria Kreps: National Research University Higher, School of Economics 3 Kantemorovkaya st., St. Petersburg, Russia2St.Petersburg Institute for Economics and Mathematics, RAS, 38 Serpuhovkaya st., St. Petersburg, Russia

International Game Theory Review (IGTR), 2017, vol. 19, issue 02, 1-7

Abstract: We consider finite noncooperative 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 noncooperative (m1 × m2 ×⋯ × mN)-games in mixed strategies such that all games of a broader vector space of noncooperative N person games on the product of unit (mi − 1)-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.

Keywords: Finite noncooperative N person games; vector space; Nash equilibrium point; maximality (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1142/S0219198917500037

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