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Best-Reply Dynamics in Large Anonymous Games

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  • Yakov Babichenko

Abstract

We consider small-influence anonymous games with a large number of players $n$ where every player has two actions. For this class of games we present a best-reply dynamic with the following two properties. First, the dynamic reaches Nash approximate equilibria fast (in at most $cn\ log n$ steps for some constant $c>0$). Second, Nash approximate equilibria are played by the dynamic with a limit frequency of at least $1-e^{-c'n}$ for some constant $c'>0$.

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  • Yakov Babichenko, 2012. "Best-Reply Dynamics in Large Anonymous Games," Discussion Paper Series dp600, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp600
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    File URL: http://ratio.huji.ac.il/sites/default/files/publications/dp600.pdf
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    1. Hart, Sergiu & Mas-Colell, Andreu, 2006. "Stochastic uncoupled dynamics and Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 57(2), pages 286-303, November.
    2. Germano, Fabrizio & Lugosi, Gabor, 2007. "Global Nash convergence of Foster and Young's regret testing," Games and Economic Behavior, Elsevier, vol. 60(1), pages 135-154, July.
    3. Sergiu Hart & Yishay Mansour, 2006. "The Communication Complexity of Uncoupled Nash Equilibrium Procedures," Levine's Bibliography 122247000000001299, UCLA Department of Economics.
    4. Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, vol. 93(5), pages 1830-1836, December.
    5. Yaron Azrieli & Eran Shmaya, 2013. "Lipschitz Games," Mathematics of Operations Research, INFORMS, vol. 38(2), pages 350-357, May.
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