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Fast Convergence in Evolutionary Equilibrium Selection

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  • H Peyton Young
  • Gabriel E. Kreindler

Abstract

Stochastic learning models provide sharp predictions about equilibrium selection when the noise level of the learning process is taken to zero. The difficulty is that, when the noise is extremely small, it can take an extremely long time for a large population to reach the stochastically stable equilibrium. An important exception arises when players interact locally in small close-knit groups; in this case convergence can be rapid for small noise and an arbitrarily large population. We show that a similar result holds when the population is fully mixed and there is no local interaction. Selection is sharp and convergence is fast when the noise level is 'fairly' small but not extremely small.

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  • H Peyton Young & Gabriel E. Kreindler, 2011. "Fast Convergence in Evolutionary Equilibrium Selection," Economics Series Working Papers 569, University of Oxford, Department of Economics.
    • Handle: RePEc:oxf:wpaper:569
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    Cited by:

    1. H Peyton Young, 2014. "The Evolution of Social Norms," Economics Series Working Papers 726, University of Oxford, Department of Economics.
    2. Sandholm, William H. & Izquierdo, Segismundo S. & Izquierdo, Luis R., 2020. "Stability for best experienced payoff dynamics," Journal of Economic Theory, Elsevier, vol. 185(C).
    3. Arigapudi, Srinivas & Heller, Yuval & Milchtaich, Igal, 2020. "Instability of Defection in the Prisoner’s Dilemma: Best Experienced Payoff Dynamics Analysis," MPRA Paper 99594, University Library of Munich, Germany.
    4. Levine, David Knudsen & Modica, Salvatore, 2016. "Dynamics in stochastic evolutionary models," Theoretical Economics, Econometric Society, vol. 11(1), January.
    5. Marden, Jason R. & Shamma, Jeff S., 2015. "Game Theory and Distributed Control****Supported AFOSR/MURI projects #FA9550-09-1-0538 and #FA9530-12-1-0359 and ONR projects #N00014-09-1-0751 and #N0014-12-1-0643," Handbook of Game Theory with Economic Applications,, Elsevier.
    6. Ascensión Andina-Díaz & José A. García-Martínez & Antonio Parravano, 2019. "The market for scoops: a dynamic approach," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 10(2), pages 175-206, June.
    7. Newton, Jonathan & Angus, Simon D., 2015. "Coalitions, tipping points and the speed of evolution," Journal of Economic Theory, Elsevier, vol. 157(C), pages 172-187.
    8. H Peyton Young & Gabriel E. Kreindler, 2012. "Rapid Innovation Diffusion in Social Networks," Economics Series Working Papers 626, University of Oxford, Department of Economics.
    9. Gallo, Edoardo, 2020. "Communication networks in markets," European Economic Review, Elsevier, vol. 129(C).
    10. Sawa, Ryoji & Wu, Jiabin, 2018. "Reference-dependent preferences, super-dominance and stochastic stability," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 96-104.
    11. Sawa, Ryoji & Wu, Jiabin, 2018. "Prospect dynamics and loss dominance," Games and Economic Behavior, Elsevier, vol. 112(C), pages 98-124.
    12. Wallace, Chris & Young, H. Peyton, 2015. "Stochastic Evolutionary Game Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    13. Vassili Kolokoltsov, 2017. "The Evolutionary Game of Pressure (or Interference), Resistance and Collaboration," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 915-944, November.
    14. Oyama, Daisuke & Sandholm, William H. & Tercieux, Olivier, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
    15. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, Open Access Journal, vol. 9(2), pages 1-1, May.
    16. Ellison, Glenn & Fudenberg, Drew & Imhof, Lorens A., 2016. "Fast convergence in evolutionary models: A Lyapunov approach," Journal of Economic Theory, Elsevier, vol. 161(C), pages 1-36.
    17. Kevin Hasker, 2014. "The Emergent Seed: A Representation Theorem for Models of Stochastic Evolution and two formulas for Waiting Time," Levine's Working Paper Archive 786969000000000954, David K. Levine.
    18. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    19. Lahkar, Ratul, 2017. "Equilibrium selection in the stag hunt game under generalized reinforcement learning," Journal of Economic Behavior & Organization, Elsevier, vol. 138(C), pages 63-68.
    20. David K Levine & Salvatore Modica, 2014. "Dynamics in Stochastic Evolutionary Models," Levine's Bibliography 786969000000000864, UCLA Department of Economics.
    21. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Sandholm, William H., 2019. "An introduction to ABED: Agent-based simulation of evolutionary game dynamics," Games and Economic Behavior, Elsevier, vol. 118(C), pages 434-462.
    22. Mercure, Jean-François, 2018. "Fashion, fads and the popularity of choices: Micro-foundations for diffusion consumer theory," Structural Change and Economic Dynamics, Elsevier, vol. 46(C), pages 194-207.
    23. Srinivas Arigapudi & Yuval Heller & Igal Milchtaich, 2020. "Instability of Defection in the Prisoner's Dilemma Under Best Experienced Payoff Dynamics," Papers 2005.05779, arXiv.org, revised Jan 2021.
    24. Itai Arieli & Yakov Babichenko & Ron Peretz & H. Peyton Young, 2020. "The Speed of Innovation Diffusion in Social Networks," Econometrica, Econometric Society, vol. 88(2), pages 569-594, March.
    25. Lim, Wooyoung & Neary, Philip R., 2016. "An experimental investigation of stochastic adjustment dynamics," Games and Economic Behavior, Elsevier, vol. 100(C), pages 208-219.

    More about this item

    Keywords

    Stochastic stability; Logit learning; Markov chain; Convergence time;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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