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On the number of pure strategy Nash equilibria in random games

Author

Listed:
  • Marco Scarsini

    () (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique, Dipartimento di Scienze Economiche e Aziendali - LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma])

  • Yosef Rinott

    (Department of Mathematics - University of California - UC Davis - University of California [Davis])

Abstract

How many pure Nash equilibria can we expect to have in a finite game chosen at random? Solutions to the above problem have been proposed in some special cases. In this paper we assume independence among the profiles, but we allow either positive or negative dependence among the players' payoffs in a same profile. We provide asymptotic results for the distribution of the number of Nash equilibria when either the number of players or the number of strategies increases. We will show that different dependence assumptions lead to different asymptotic results.

Suggested Citation

  • Marco Scarsini & Yosef Rinott, 2000. "On the number of pure strategy Nash equilibria in random games," Post-Print hal-00540207, HAL.
  • Handle: RePEc:hal:journl:hal-00540207
    DOI: 10.1006/game.1999.0775
    Note: View the original document on HAL open archive server: https://hal-hec.archives-ouvertes.fr/hal-00540207
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    References listed on IDEAS

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    1. Stanford, William, 1997. "On the distribution of pure strategy equilibria in finite games with vector payoffs," Mathematical Social Sciences, Elsevier, vol. 33(2), pages 115-127, April.
    2. Stanford, William, 1999. "On the number of pure strategy Nash equilibria in finite common payoffs games," Economics Letters, Elsevier, vol. 62(1), pages 29-34, January.
    3. 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. Porter, Ryan & Nudelman, Eugene & Shoham, Yoav, 2008. "Simple search methods for finding a Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 63(2), pages 642-662, July.
    2. Stanford, William, 2010. "The number of pure strategy Nash equilibria in random multi-team games," Economics Letters, Elsevier, vol. 108(3), pages 352-354, September.
    3. Collevecchio, Andrea & LiCalzi, Marco, 2012. "The probability of nontrivial common knowledge," Games and Economic Behavior, Elsevier, vol. 76(2), pages 556-570.
    4. Rinott, Yosef & Rotar, Vladimir, 2001. "A remark on quadrant normal probabilities in high dimensions," Statistics & Probability Letters, Elsevier, vol. 51(1), pages 47-51, January.
    5. Takahashi, Satoru, 2008. "The number of pure Nash equilibria in a random game with nondecreasing best responses," Games and Economic Behavior, Elsevier, vol. 63(1), pages 328-340, May.
    6. Arieli, Itai & Babichenko, Yakov, 2016. "Random extensive form games," Journal of Economic Theory, Elsevier, vol. 166(C), pages 517-535.

    More about this item

    Keywords

    Games; strategy; equilibria;

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