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Symmetric multi-person zero-sum game with two sets of strategic variables

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  • Satoh, Atsuhiro
  • Tanaka, Yasuhito

Abstract

We consider a symmetric multi-person zero-sum game with two sets of alternative strategic variables which are related by invertible functions. They are denoted by (s1, s2, ..., sn) and (t1, t2, ..., tn) for players 1, 2, ..., n. The number of players is larger than two. We consider a symmetric game in the sense that all players have the same payoff functions. We do not postulate differentiability of the payoff functions of players. We will show that the following patterns of competition, 1) all players choose si, 2) all players choose ti and 3) m players choose ti, i=1, ..., m and n-m players choose sj, j=m+1, ..., n where 1

Suggested Citation

  • Satoh, Atsuhiro & Tanaka, Yasuhito, 2016. "Symmetric multi-person zero-sum game with two sets of strategic variables," MPRA Paper 75838, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:75838
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    References listed on IDEAS

    as
    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. 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. 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.
    5. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Relative profit maximization in asymmetric oligopoly," Economics Bulletin, AccessEcon, vol. 34(3), pages 1653-1664.
    6. Satoh, Atsuhiro & Tanaka, Yasuhito, 2014. "Relative profit maximization in asymmetric oligopoly: Cournot and Bertrand equilibria," MPRA Paper 55883, University Library of Munich, Germany.
    7. 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.
    8. 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.
    9. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    10. Satoh, Atsuhiro & Tanaka, Yasuhito, 2016. "Maximin and minimax strategies in symmetric oligopoly: Cournot and Bertrand," MPRA Paper 75837, University Library of Munich, Germany.
    11. 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.
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    Cited by:

    1. Satoh, Atsuhiro & Tanaka, Yasuhito, 2016. "Maximin and minimax strategies in symmetric oligopoly: Cournot and Bertrand," MPRA Paper 75837, University Library of Munich, Germany.

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    More about this item

    Keywords

    multi-person zero-sum game; two strategic variables;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection

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