Maximin and Minimax Strategies in Two-Players Game with Two Strategic Variables

Atsuhiro Satoh () and Yasuhito Tanaka

International Game Theory Review (IGTR), 2018, vol. 20, issue 01, 1-13

Abstract: We examine maximin and minimax strategies for players in a two-players game with two strategic variables, x and p. We consider two patterns of game; one is the x-game in which the strategic variables of players are x’s, and the other is the p-game in which the strategic variables of players are p’s. We call two players Players A and B, and will show that the maximin strategy and the minimax strategy in the x-game, and the maximin strategy and the minimax strategy in the p-game are all equivalent for each player. However, the maximin strategy for Player A and that for Player B are not necessarily equivalent, and they are not necessarily equivalent to their Nash equilibrium strategies in the x-game nor the p-game. But, in a special case, where the objective function of Player B is the opposite of the objective function of Player A, the maximin strategy for Player A and that for Player B are equivalent, and they constitute the Nash equilibrium both in the x-game and the p-game.

Keywords: Two-players game; two strategic variables; maximin strategy; minimax strategy (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S021919891750030X

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