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


  • McLennan, A
  • Park, I-U


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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    References listed on IDEAS

    1. McKelvey, Richard D. & McLennan, Andrew, 1997. "The Maximal Number of Regular Totally Mixed Nash Equilibria," Journal of Economic Theory, Elsevier, vol. 72(2), pages 411-425, February.
    2. McLennan, Andrew, 1997. "The Maximal Generic Number of Pure Nash Equilibria," Journal of Economic Theory, Elsevier, vol. 72(2), pages 408-410, February.
    3. Keiding, Hans, 1997. "On the Maximal Number of Nash Equilibria in ann x nBimatrix Game," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 148-160, October.
    4. Powers, Imelda Yeung, 1990. "Limiting Distributions of the Number of Pure Strategy Nash Equilibria in N-Person Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(3), pages 277-286.
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    Cited by:

    1. Ɖura-Georg Granić & Johannes Kern, 2016. "Circulant games," Theory and Decision, Springer, vol. 80(1), pages 43-69, January.
    2. Honda, Jun, 2015. "Games with the Total Bandwagon Property," Department of Economics Working Paper Series 4582, WU Vienna University of Economics and Business.
    3. 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.
    4. 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.
    5. 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.
    6. von Stengel, Bernhard & Savani, Rahul, 2016. "Unit vector games," LSE Research Online Documents on Economics 65506, London School of Economics and Political Science, LSE Library.
    7. Philip V. Fellman & Jonathan Vos Post, 2007. "Quantum Nash Equilibria and Quantum Computing," Papers 0707.0324,
    8. Jun Honda, 2015. "Games with the Total Bandwagon Property," Department of Economics Working Papers wuwp197, Vienna University of Economics and Business, Department of Economics.

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    JEL classification:

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


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