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Asymptotic expected number of Nash equilibria of two-player normal form games

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  • McLennan, Andrew
  • Berg, Johannes

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  • 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.
    • Handle: RePEc:eee:gamebe:v:51:y:2005:i:2:p:264-295
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    References listed on IDEAS

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    1. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759, Elsevier.
    2. Gilboa, Itzhak & Zemel, Eitan, 1989. "Nash and correlated equilibria: Some complexity considerations," Games and Economic Behavior, Elsevier, vol. 1(1), pages 80-93, March.
    3. Andrew McLennan, 2005. "The Expected Number of Nash Equilibria of a Normal Form Game," Econometrica, Econometric Society, vol. 73(1), pages 141-174, January.
    4. 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.
    5. McLennan, Andrew & Park, In-Uck, 1999. "Generic 4 x 4 Two Person Games Have at Most 15 Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 26(1), pages 111-130, January.
    6. 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:

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    2. Tom Johnston & Michael Savery & Alex Scott & Bassel Tarbush, 2023. "Game Connectivity and Adaptive Dynamics," Papers 2309.10609, arXiv.org, revised Nov 2023.
    3. Bade, Sophie & Haeringer, Guillaume & Renou, Ludovic, 2007. "More strategies, more Nash equilibria," Journal of Economic Theory, Elsevier, vol. 135(1), pages 551-557, July.
    4. Brandl, Florian, 2017. "The distribution of optimal strategies in symmetric zero-sum games," Games and Economic Behavior, Elsevier, vol. 104(C), pages 674-680.
    5. Pei, Ting & Takahashi, Satoru, 2019. "Rationalizable strategies in random games," Games and Economic Behavior, Elsevier, vol. 118(C), pages 110-125.
    6. Conitzer, Vincent & Sandholm, Tuomas, 2008. "New complexity results about Nash equilibria," Games and Economic Behavior, Elsevier, vol. 63(2), pages 621-641, July.
    7. Carvalho, Margarida & Lodi, Andrea & Pedroso, João.P., 2022. "Computing equilibria for integer programming games," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1057-1070.
    8. 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.
    9. Manh Hong Duong & The Anh Han, 2016. "On the Expected Number of Equilibria in a Multi-player Multi-strategy Evolutionary Game," Dynamic Games and Applications, Springer, vol. 6(3), pages 324-346, September.
    10. Klaus Kultti & Hannu Salonen & Hannu Vartiainen, 2011. "Distribution of pure Nash equilibria in n-person games with random best replies," Discussion Papers 71, Aboa Centre for Economics.
    11. Patrick Bajari & Han Hong & Stephen P. Ryan, 2010. "Identification and Estimation of a Discrete Game of Complete Information," Econometrica, Econometric Society, vol. 78(5), pages 1529-1568, September.
    12. Elizabeth Baldwin & Paul Klemperer, 2019. "Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities," Econometrica, Econometric Society, vol. 87(3), pages 867-932, May.
    13. Arieli, Itai & Babichenko, Yakov, 2016. "Random extensive form games," Journal of Economic Theory, Elsevier, vol. 166(C), pages 517-535.
    14. Lee, Robin S. & Pakes, Ariel, 2009. "Multiple equilibria and selection by learning in an applied setting," Economics Letters, Elsevier, vol. 104(1), pages 13-16, July.
    15. 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.
    16. Torsten Heinrich & Yoojin Jang & Luca Mungo & Marco Pangallo & Alex Scott & Bassel Tarbush & Samuel Wiese, 2023. "Best-response dynamics, playing sequences, and convergence to equilibrium in random games," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 703-735, September.
    17. Martin Bichler & Zhen Hao & Gediminas Adomavicius, 2017. "Coalition-Based Pricing in Ascending Combinatorial Auctions," Information Systems Research, INFORMS, vol. 28(1), pages 159-179, March.
    18. Torsten Heinrich & Yoojin Jang & Luca Mungo & Marco Pangallo & Alex Scott & Bassel Tarbush & Samuel Wiese, 2021. "Best-response dynamics, playing sequences, and convergence to equilibrium in random games," Papers 2101.04222, arXiv.org, revised Nov 2022.
    19. Pangallo, Marco & Heinrich, Torsten & Jang, Yoojin & Scott, Alex & Tarbush, Bassel & Wiese, Samuel & Mungo, Luca, 2021. "Best-Response Dynamics, Playing Sequences, And Convergence To Equilibrium In Random Games," INET Oxford Working Papers 2021-23, Institute for New Economic Thinking at the Oxford Martin School, University of Oxford.
    20. 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.
    21. Samuel C. Wiese & Torsten Heinrich, 2022. "The Frequency of Convergent Games under Best-Response Dynamics," Dynamic Games and Applications, Springer, vol. 12(2), pages 689-700, June.
    22. David Roberts, 2006. "Nash equilibria of Cauchy-random zero-sum and coordination matrix games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(2), pages 167-184, August.
    23. Misha Gavrilovich & Victoriya Kreps, 2015. "On a Class of Optimization Problems with No “Effectively Computable” Solution," HSE Working papers WP BRP 112/EC/2015, National Research University Higher School of Economics.

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