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A Bound on the Number of Nash Equilibria in a Coordination Game

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Abstract

We prove that a "nondegenerate" m x m coordination game can have at most 2^{M} - 1 Nash equilibria, where M = min(m,n).

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  • Thomas Quint & Martin Shubik, 1995. "A Bound on the Number of Nash Equilibria in a Coordination Game," Cowles Foundation Discussion Papers 1095, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1095
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    References listed on IDEAS

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    1. B. Curtis Eaves, 1971. "The Linear Complementarity Problem," Management Science, INFORMS, vol. 17(9), pages 612-634, May.
    2. M. J. M. Jansen, 1981. "Regularity and Stability of Equilibrium Points of Bimatrix Games," Mathematics of Operations Research, INFORMS, vol. 6(4), pages 530-550, November.
    3. Thomas Quint & Martin Shubik, 1994. "On the Number of Nash Equilibria in a Bimatrix Game," Cowles Foundation Discussion Papers 1089, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. Philip V. Fellman & Jonathan Vos Post, 2007. "Quantum Nash Equilibria and Quantum Computing," Papers 0707.0324, arXiv.org.
    2. Jun Honda, 2018. "Games with the total bandwagon property meet the Quint–Shubik conjecture," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 893-912, September.
    3. Ɖura-Georg Granić & Johannes Kern, 2016. "Circulant games," Theory and Decision, Springer, vol. 80(1), pages 43-69, January.
    4. Ravi Kannan & Thorsten Theobald, 2010. "Games of fixed rank: a hierarchy of bimatrix games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 157-173, January.
    5. Thomas Quint & Martin Shubik, 1994. "On the Number of Nash Equilibria in a Bimatrix Game," Cowles Foundation Discussion Papers 1089, Cowles Foundation for Research in Economics, Yale University.
    6. Hwang, Sung-Ha & Rey-Bellet, Luc, 2020. "Strategic decompositions of normal form games: Zero-sum games and potential games," Games and Economic Behavior, Elsevier, vol. 122(C), pages 370-390.

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