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

Author

Listed:
  • Atsuhiro Satoh

    (Faculty of Economics, Hokkai-Gakuen University, Toyohira-ku, Sapporo, Hokkaido 062-8605, Japan)

  • Yasuhito Tanaka

    (Faculty of Economics, Doshisha University, Kamigyo-ku, Kyoto 602-8580, Japan)

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.

Suggested Citation

  • Atsuhiro Satoh & Yasuhito Tanaka, 2018. "Maximin and Minimax Strategies in Two-Players Game with Two Strategic Variables," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-13, March.
    • Handle: RePEc:wsi:igtrxx:v:20:y:2018:i:01:n:s021919891750030x
    DOI: 10.1142/S021919891750030X
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    References listed on IDEAS

    as
    1. Toshihiro Matsumura & Noriaki Matsushima, 2012. "Competitiveness And Stability Of Collusive Behavior," Bulletin of Economic Research, Wiley Blackwell, vol. 64(Supplemen), pages 22-31, December.
    2. Yasuhito Tanaka, 2013. "Irrelevance of the choice of strategic variables in duopoly under relative profit maximization," Economics and Business Letters, Oviedo University Press, vol. 2(2), pages 75-83.
    3. Yasuhito Tanaka, 2013. "Equivalance of Cournot and Bertrand equilibria in differentiated duopoly under relative profit maximization with linear demand," Economics Bulletin, AccessEcon, vol. 33(2), pages 1479-1486.
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    5. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Relative profit maximization in asymmetric oligopoly," Economics Bulletin, AccessEcon, vol. 34(3), pages 1653-1664.
    6. Atsuhiro Satoh & Yasuhito Tanaka, 2019. "Two Person Zero-Sum Game with Two Sets of Strategic Variables," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 21(03), pages 1-15, September.
    7. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    8. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Relative profit maximization and equivalence of Cournot and Bertrand equilibria in asymmetric duopoly," Economics Bulletin, AccessEcon, vol. 34(2), pages 819-827.
    9. Satoh, Atsuhiro & Tanaka, Yasuhito, 2016. "Choice of Strategic Variables by Relative Profit Maximizing Firms in Oligopoly," Economic Review, Hitotsubashi University, vol. 67(1), pages 17-25, January.
    10. Matsumura, Toshihiro & Matsushima, Noriaki & Cato, Susumu, 2013. "Competitiveness and R&D competition revisited," Economic Modelling, Elsevier, vol. 31(C), pages 541-547.
    Full references (including those not matched with items on IDEAS)

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