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On the equivalence of Stackelberg equilibrium and static equilibrium of symmetric multi-players zero-sum game

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  • Tanaka, Yasuhito

Abstract

We study a Stackelberg type symmetric dynamic multi-players zero-sum game. One player is the leader and other players are followers. All players have symmetric payoff functions. The game is a two-stages game. In the first stage the leader determines the value of its strategic variable. In the second stage the followers determine the values of their strategic variables given the value of the leader's strategic variable. On the other hand, in the static game all players simultaneously determine the values of their strategic variables. We show that if and only if the game is fully symmetric, the Stackelberg equilibrium and the static equilibrium are equivalent.

Suggested Citation

  • Tanaka, Yasuhito, 2019. "On the equivalence of Stackelberg equilibrium and static equilibrium of symmetric multi-players zero-sum game," MPRA Paper 91897, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:91897
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    References listed on IDEAS

    as
    1. PONSSARD, Jean-Pierre & ZAMIR, Shmuel, 1973. "Zero-sum sequential games with incomplete information," LIDAM Reprints CORE 149, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Matsumura, Toshihiro & Matsushima, Noriaki & Cato, Susumu, 2013. "Competitiveness and R&D competition revisited," Economic Modelling, Elsevier, vol. 31(C), pages 541-547.
    3. Atsuhiro Satoh & Yasuhito Tanaka, 2014. "Relative profit maximization in asymmetric oligopoly," Economics Bulletin, AccessEcon, vol. 34(3), pages 1653-1664.
    4. Satoh, Atsuhiro & Tanaka, Yasuhito, 2014. "Relative profit maximization in asymmetric oligopoly: Cournot and Bertrand equilibria," MPRA Paper 55883, University Library of Munich, Germany.
    5. 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.
    6. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    7. Tanaka, Yasuhito, 2014. "Relative profit maximization and irrelevance of leadership in Stackelberg model," MPRA Paper 55887, University Library of Munich, Germany.
    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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Stackelberg equilibrium; static equilibrium; multi-players zero-sum game;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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