Satoh, Atsuhiro and Tanaka, Yasuhito (2018): On zerosum game formulation of non zerosum game.

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Abstract
We consider a formulation of a non zerosum n players game by an n+1 players zerosum game. We suppose the existence of the n+1th player in addition to n players in the main game, and virtual subsidies to the n players which is provided by the n+1th player. Its strategic variable affects only the subsidies, and does not affect choice of strategies by the n players in the main game. His objective function is the opposite of the sum of the payoffs of the n players. We will show 1) The minimax theorem by Sion (Sion(1958)) implies the existence of Nash equilibrium in the n players non zerosum game. 2) The maximin strategy of each player in {1, 2, ..., n} with the minimax strategy of the n+1th player is equivalent to the Nash equilibrium strategy of the n players non zerosum game. 3) The existence of Nash equilibrium in the n players non zerosum game implies Sion's minimax theorem for pairs of each of the n players and the n+1th player.
Item Type:  MPRA Paper 

Original Title:  On zerosum game formulation of non zerosum game 
Language:  English 
Keywords:  zerosum game, non zerosum game, minimax theorem, virtual subsidy 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  88976 
Depositing User:  Yasuhito Tanaka 
Date Deposited:  15 Sep 2018 07:15 
Last Modified:  26 Sep 2019 20:56 
References:  Kindler, J. (2005), ``A simple proof of Sion's minimax theorem,'' American Mathematical Monthly, 112, pp. 356358. Komiya, H. (1988), ``Elementary proof for Sion's minimax theorem,'' Kodai Mathematical Journal, 11, pp. 57. Sion, M. (1958), ``On general minimax theorems,'' Pacific Journal of Mathematics, 8, pp. 171176. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/88976 