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The pure Nash equilibrium property and the quasi-acyclic condition

Author

Listed:
  • Tetsuo Yamamori

    (Graduate School of Economics, University of Tokyo)

  • Satoru Takahashi

    (Department of Economics, Harvard University)

Abstract

This paper presents a sufficient condition for the quasi-acyclic condition. A game is quasi-acyclic if from any strategy profile, there exists a finite sequence of strict best replies that ends in a pure strategy Nash equilibrium. The best-reply dynamics must converge to a pure strategy Nash equilibrium in any quasi-acyclic game. A game has the pure Nash equilibrium property (PNEP) if there is a pure strategy Nash equilibrium in any game constructed by restricting the set of strategies to a subset of the set of strategies in the original game. Any finite, ordinal potential game and any finite, supermodular game have the PNEP. We show that any finite, two-player game with the PNEP is quasi-acyclic.

Suggested Citation

  • Tetsuo Yamamori & Satoru Takahashi, 2002. "The pure Nash equilibrium property and the quasi-acyclic condition," Economics Bulletin, AccessEcon, vol. 3(22), pages 1-6.
    • Handle: RePEc:ebl:ecbull:eb-02c70011
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    Citations

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    Cited by:

    1. Tom Johnston & Michael Savery & Alex Scott & Bassel Tarbush, 2023. "Game Connectivity and Adaptive Dynamics," Papers 2309.10609, arXiv.org, revised Oct 2024.
    2. Lu Yu, 2024. "Existence and structure of Nash equilibria for supermodular games," Papers 2406.09582, arXiv.org.
    3. Torsten Heinrich & Yoojin Jang & Luca Mungo & Marco Pangallo & Alex Scott & Bassel Tarbush & Samuel Wiese, 2023. "Best-response dynamics, playing sequences, and convergence to equilibrium in random games," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 703-735, September.
    4. Torsten Heinrich & Yoojin Jang & Luca Mungo & Marco Pangallo & Alex Scott & Bassel Tarbush & Samuel Wiese, 2021. "Best-response dynamics, playing sequences, and convergence to equilibrium in random games," Papers 2101.04222, arXiv.org, revised Nov 2022.
    5. Endre Boros & Khaled Elbassioni & Vladimir Gurvich & Kazuhisa Makino & Vladimir Oudalov, 2016. "Sufficient conditions for the existence of Nash equilibria in bimatrix games in terms of forbidden $$2 \times 2$$ 2 × 2 subgames," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 1111-1131, November.
    6. Berger, Ulrich, 2007. "Two more classes of games with the continuous-time fictitious play property," Games and Economic Behavior, Elsevier, vol. 60(2), pages 247-261, August.
    7. repec:ebl:ecbull:v:3:y:2007:i:33:p:1-5 is not listed on IDEAS
    8. Ben Amiet & Andrea Collevecchio & Kais Hamza, 2020. "When "Better" is better than "Best"," Papers 2011.00239, arXiv.org.
    9. Pangallo, Marco & Heinrich, Torsten & Jang, Yoojin & Scott, Alex & Tarbush, Bassel & Wiese, Samuel & Mungo, Luca, 2021. "Best-Response Dynamics, Playing Sequences, And Convergence To Equilibrium In Random Games," INET Oxford Working Papers 2021-23, Institute for New Economic Thinking at the Oxford Martin School, University of Oxford.
    10. Ulrich Berger, 2004. "Two More Classes of Games with the Fictitious Play Property," Game Theory and Information 0408003, University Library of Munich, Germany.
    11. Nikolai S. Kukushkin, 2007. "Shapley's "2 by 2" theorem for game forms," Economics Bulletin, AccessEcon, vol. 3(33), pages 1-5.

    More about this item

    Keywords

    best-reply dynamics;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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