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When "Better" is better than "Best"

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  • Ben Amiet
  • Andrea Collevecchio
  • Kais Hamza

Abstract

We consider two-player normal form games where each player has the same finite strategy set. The payoffs of each player are assumed to be i.i.d. random variables with a continuous distribution. We show that, with high probability, the better-response dynamics converge to pure Nash equilibrium whenever there is one, whereas best-response dynamics fails to converge, as it is trapped.

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  • Ben Amiet & Andrea Collevecchio & Kais Hamza, 2020. "When "Better" is better than "Best"," Papers 2011.00239, arXiv.org.
    • Handle: RePEc:arx:papers:2011.00239
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    References listed on IDEAS

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    1. Rinott, Yosef & Scarsini, Marco, 2000. "On the Number of Pure Strategy Nash Equilibria in Random Games," Games and Economic Behavior, Elsevier, vol. 33(2), pages 274-293, November.
    2. Kukushkin, Nikolai S., 2018. "Better response dynamics and Nash equilibrium in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 68-78.
    3. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    4. Ben Amiet & Andrea Collevecchio & Marco Scarsini & Ziwen Zhong, 2021. "Pure Nash Equilibria and Best-Response Dynamics in Random Games," Mathematics of Operations Research, INFORMS, vol. 46(4), pages 1552-1572, November.
    5. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    6. repec:ebl:ecbull:v:3:y:2002:i:22:p:1-6 is not listed on IDEAS
    7. Friedman, James W. & Mezzetti, Claudio, 2001. "Learning in Games by Random Sampling," Journal of Economic Theory, Elsevier, vol. 98(1), pages 55-84, May.
    8. Philip Reny, 2011. "Strategic approximations of discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 17-29, September.
    9. 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.
    10. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    11. Cabrales, Antonio & Serrano, Roberto, 2011. "Implementation in adaptive better-response dynamics: Towards a general theory of bounded rationality in mechanisms," Games and Economic Behavior, Elsevier, vol. 73(2), pages 360-374.
    12. Tetsuo Yamamori & Satoru Takahashi, 2002. "The pure Nash equilibrium property and the quasi-acyclic condition," Economics Bulletin, AccessEcon, vol. 3(22), pages 1-6.
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