On zero-sum game formulation of non zero-sum game

Atsuhiro Satoh () and Yasuhito Tanaka

MPRA Paper from University Library of Munich, Germany

Abstract: We consider a formulation of a non zero-sum n players game by an n+1 players zero-sum game. We suppose the existence of the n+1-th player in addition to n players in the main game, and virtual subsidies to the n players which is provided by the n+1-th 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 zero-sum game. 2) The maximin strategy of each player in {1, 2, ..., n} with the minimax strategy of the n+1-th player is equivalent to the Nash equilibrium strategy of the n players non zero-sum game. 3) The existence of Nash equilibrium in the n players non zero-sum game implies Sion's minimax theorem for pairs of each of the n players and the n+1-th player.

Keywords: zero-sum game; non zero-sum game; minimax theorem; virtual subsidy (search for similar items in EconPapers)
JEL-codes: C72 (search for similar items in EconPapers)
Date: 2018-09-13
New Economics Papers: this item is included in nep-gth, nep-hpe and nep-mic
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