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Two person zero-sum game with two sets of strategic variables

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  • Satoh, Atsuhiro
  • Tanaka, Yasuhito

Abstract

We consider a two-person zero-sum game with two sets of strategic variables which are related by invertible functions. They are denoted by (sA, sB) and (tA, tB) for players A and B. We will show that the following four patterns of competition are equivalent, that is, they yield the same outcome. 1. Player A and B choose sA and sB (competition by (sA, sB)). 2. Player A and B choose tA and tB (competition by (tA, tB)). 3. Player A and B choose tA and sB (competition by (tA, sB)). 4. Player A and B choose sA and tB (competition by (sA, tB)).

Suggested Citation

  • Satoh, Atsuhiro & Tanaka, Yasuhito, 2016. "Two person zero-sum game with two sets of strategic variables," MPRA Paper 73272, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:73272
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    References listed on IDEAS

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    1. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    2. Matsumura, Toshihiro & Matsushima, Noriaki & Cato, Susumu, 2013. "Competitiveness and R&D competition revisited," Economic Modelling, Elsevier, vol. 31(C), pages 541-547.
    3. 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.
    4. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Relative profit maximization in asymmetric oligopoly," Economics Bulletin, AccessEcon, vol. 34(3), pages 1653-1664.
    5. Satoh, Atsuhiro & Tanaka, Yasuhito, 2014. "Relative profit maximization in asymmetric oligopoly: Cournot and Bertrand equilibria," MPRA Paper 55883, University Library of Munich, Germany.
    6. 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.
    7. Atsuhiro Satoh & Yasuhito Tanaka, 2013. "Relative profit maximization and Bertrand equilibrium with quadratic cost functions," Economics and Business Letters, Oviedo University Press, vol. 2(3), pages 134-139.
    8. Satoh, Atsuhiro & Tanaka, Yasuhito, 2014. "Relative profit maximization and equivalence of Cournot and Bertrand equilibria in an asymmetric differentiated duopoly," MPRA Paper 55895, University Library of Munich, Germany.
    9. Satoh, Atsuhiro & Tanaka, Yasuhito, 2014. "Choice of strategic variables under relative profit maximization in asymmetric oligopoly," MPRA Paper 55886, University Library of Munich, Germany.
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    Cited by:

    1. Tanaka, Yasuhito & Satoh, Atsuhiro, 2016. "Maximin and minimax strategies in asymmetric duopoly: Cournot and Bertrand," MPRA Paper 73925, University Library of Munich, Germany.
    2. Masahiko Hattori & Atsuhiro Satoh & Yasuhito Tanaka, 2018. "Minimax theorem and Nash equilibrium of symmetric multi-players zero-sum game with two strategic variables," Papers 1806.07203, arXiv.org.
    3. Hattori, Masahiko & Satoh, Atsuhiro & Tanaka, Yasuhito, 2018. "Minimax theorem and Nash equilibrium of symmetric three-players zero-sum game with two strategic variables," MPRA Paper 85503, University Library of Munich, Germany.
    4. Atsuhiro Satoh & Yasuhito Tanaka, 2018. "Nash equilibrium of partially asymmetric three-players zero-sum game with two strategic variables," Papers 1809.02465, arXiv.org.
    5. Satoh, Atsuhiro & Tanaka, Yasuhito, 2018. "Nash equilibrium in asymmetric multi-players zero-sum game with two strategic variables and only one alien," MPRA Paper 88978, University Library of Munich, Germany.
    6. Satoh, Atsuhiro & Tanaka, Yasuhito, 2016. "Maximin and minimax strategies in symmetric oligopoly: Cournot and Bertrand," MPRA Paper 75837, University Library of Munich, Germany.
    7. 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.

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    More about this item

    Keywords

    zero-sum game; two strategic variables; equivalence of outcome;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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