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Stochastic Learning Dynamics and Speed of Convergence in Population Games

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  • Itai Arieli
  • H. Peyton Young

Abstract

We study how long it takes for large populations of interacting agents to come close to Nash equilibrium when they adapt their behavior using a stochastic better reply dynamic. Prior work considers this question mainly for 2 × 2 games and potential games; here we characterize convergence times for general weakly acyclic games, including coordination games, dominance solvable games, games with strategic complementarities, potential games, and many others with applications in economics, biology, and distributed control. If players' better replies are governed by idiosyncratic shocks, the convergence time can grow exponentially in the population size; moreover, this is true even in games with very simple payoff structures. However, if their responses are sufficiently correlated due to aggregate shocks, the convergence time is greatly accelerated; in fact, it is bounded for all sufficiently large populations. We provide explicit bounds on the speed of convergence as a function of key structural parameters including the number of strategies, the length of the better reply paths, the extent to which players can influence the payoffs of others, and the desired degree of approximation to Nash equilibrium.

Suggested Citation

  • Itai Arieli & H. Peyton Young, 2016. "Stochastic Learning Dynamics and Speed of Convergence in Population Games," Econometrica, Econometric Society, vol. 84, pages 627-676, March.
    • Handle: RePEc:wly:emetrp:v:84:y:2016:i::p:627-676
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    Cited by:

    1. Tom Johnston & Michael Savery & Alex Scott & Bassel Tarbush, 2023. "Game Connectivity and Adaptive Dynamics," Papers 2309.10609, arXiv.org, revised Nov 2023.
    2. Srinivas Arigapudi & Omer Edhan & Yuval Heller & Ziv Hellman, 2022. "Mentors and Recombinators: Multi-Dimensional Social Learning," Papers 2205.00278, arXiv.org, revised Nov 2023.
    3. Itai Arieli & Yakov Babichenko & Ron Peretz & H. Peyton Young, 2018. "The Speed of Innovation Diffusion," Economics Papers 2018-W06, Economics Group, Nuffield College, University of Oxford.
    4. Tsakas, Nikolas, 2017. "Diffusion by imitation: The importance of targeting agents," Journal of Economic Behavior & Organization, Elsevier, vol. 139(C), pages 118-151.
    5. Bary S. R. Pradelski & Heinrich H. Nax, 2020. "Market sentiments and convergence dynamics in decentralized assignment economies," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 275-298, March.
    6. Pangallo, Marco & Farmer, J. Doyne & Sanders, James & Galla, Tobias, 2017. "A taxonomy of learning dynamics in 2 × 2 games," INET Oxford Working Papers 2017-06, Institute for New Economic Thinking at the Oxford Martin School, University of Oxford.
    7. Iwan Bos & Marco A. Marini & Riccardo D. Saulle, 2021. "Myopic Oligopoly Pricing," "Marco Fanno" Working Papers 0271, Dipartimento di Scienze Economiche "Marco Fanno".
    8. Pangallo, Marco & Sanders, James B.T. & Galla, Tobias & Farmer, J. Doyne, 2022. "Towards a taxonomy of learning dynamics in 2 × 2 games," Games and Economic Behavior, Elsevier, vol. 132(C), pages 1-21.
    9. Arieli, Itai & Babichenko, Yakov & Peretz, Ron & Young, H. Peyton, 2020. "The speed of innovation diffusion in social networks," LSE Research Online Documents on Economics 102538, London School of Economics and Political Science, LSE Library.
    10. Yakov Babichenko, 2018. "Fast Convergence of Best-Reply Dynamics in Aggregative Games," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 333-346, February.
    11. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    12. 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.

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