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Generic 4 x 4 Two Person Games Have at Most 15 Nash Equilibria

Author

Listed:
  • McLennan, A
  • Park, I-U

Abstract

The maximal generic number of Nash equilibria for two person games in which the two agents each have four pure strategies is shown to be 15. In contrast to Keiding (1995), who arrives at this result by computer enumeration, our argument is based on a collection of lemmas that constrain the set of equilibria. Several of these pertain to any common number d of pure strategies for the two agents.

Suggested Citation

  • McLennan, A & Park, I-U, 1997. "Generic 4 x 4 Two Person Games Have at Most 15 Nash Equilibria," Papers 300, Minnesota - Center for Economic Research.
    • Handle: RePEc:fth:minner:300
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    Citations

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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. Sun, Ching-jen, 2020. "A sandwich theorem for generic n × n two person games," Games and Economic Behavior, Elsevier, vol. 120(C), pages 86-95.
    4. Jun Honda, 2015. "Games with the Total Bandwagon Property," Department of Economics Working Papers wuwp197, Vienna University of Economics and Business, Department of Economics.
    5. Conitzer, Vincent & Sandholm, Tuomas, 2008. "New complexity results about Nash equilibria," Games and Economic Behavior, Elsevier, vol. 63(2), pages 621-641, July.
    6. McLennan, Andrew & Berg, Johannes, 2005. "Asymptotic expected number of Nash equilibria of two-player normal form games," Games and Economic Behavior, Elsevier, vol. 51(2), pages 264-295, May.
    7. Rahul Savani & Bernhard von Stengel, 2016. "Unit vector games," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(1), pages 7-27, March.
    8. 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.
    9. Philip V. Fellman & Jonathan Vos Post, 2007. "Quantum Nash Equilibria and Quantum Computing," Papers 0707.0324, arXiv.org.
    10. M. Punniyamoorthy & Sarin Abraham & Jose Joy Thoppan, 2023. "A Method to Select Best Among Multi-Nash Equilibria," Studies in Microeconomics, , vol. 11(1), pages 101-127, April.
    11. 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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    Keywords

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    JEL classification:

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

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