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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. 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.
    2. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    3. 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.
    4. Matsumura, Toshihiro & Matsushima, Noriaki & Cato, Susumu, 2013. "Competitiveness and R&D competition revisited," Economic Modelling, Elsevier, vol. 31(C), pages 541-547.
    5. 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.
    6. Toshihiro Matsumura & Noriaki Matsushima, 2012. "Competitiveness And Stability Of Collusive Behavior," Bulletin of Economic Research, Wiley Blackwell, vol. 64(Supplemen), pages 22-31, December.
    7. repec:bla:buecrs:v:64:y:2012:i::p:s22-s31 is not listed on IDEAS
    8. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Relative profit maximization in asymmetric oligopoly," Economics Bulletin, AccessEcon, vol. 34(3), pages 1653-1664.
    9. 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.
    10. 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.
    Full references (including those not matched with items on IDEAS)

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