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Nash equilibrium in asymmetric multi-players zero-sum game with two strategic variables and only one alien

Atsuhiro Satoh () and Yasuhito Tanaka ()

MPRA Paper from University Library of Munich, Germany

Abstract: We consider a partially asymmetric multi-players zero-sum game with two strategic variables. All but one players have the same payoff functions, and one player (Player $n$) does not. Two strategic variables are t_i's and s_i's for each player i. Mainly we will show the following results. 1) The equilibrium when all players choose t_i's is equivalent to the equilibrium when all but one players choose t_i's and Player n chooses s_n as their strategic variables. 2) The equilibrium when all players choose s_i's is equivalent to the equilibrium when all but one players choose s_i's and Player n chooses t_n as their strategic variables. The equilibrium when all players choose t_i's and the equilibrium when all players choose s_i's are not equivalent although they are equivalent in a symmetric game in which all players have the same payoff functions.

Keywords: partially asymmetric multi-players zero-sum game; Nash equilibrium; two strategic variables (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth and nep-mic
Date: 2018-09-13
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