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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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    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. 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.
    2. Ɖura-Georg Granić & Johannes Kern, 2016. "Circulant games," Theory and Decision, Springer, vol. 80(1), pages 43-69, January.
    3. 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.
    4. Philip V. Fellman & Jonathan Vos Post, 2007. "Quantum Nash Equilibria and Quantum Computing," Papers 0707.0324, arXiv.org.
    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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