IDEAS home Printed from https://ideas.repec.org/a/wly/emetrp/v84y2016ip627-676.html
   My bibliography  Save this article

Stochastic Learning Dynamics and Speed of Convergence in Population Games

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tom Johnston & Michael Savery & Alex Scott & Bassel Tarbush, 2023. "Game Connectivity and Adaptive Dynamics," Papers 2309.10609, arXiv.org, revised Oct 2024.
    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. Bary S. R. Pradelski & Bassel Tarbush, 2024. "Satisficing Equilibrium," Papers 2409.00832, arXiv.org.
    7. 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.
    8. Bos, Iwan & Marini, Marco A. & Saulle, Riccardo D., 2024. "Myopic oligopoly pricing," Games and Economic Behavior, Elsevier, vol. 145(C), pages 377-412.
    9. 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.
    10. 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.
    11. Yakov Babichenko, 2018. "Fast Convergence of Best-Reply Dynamics in Aggregative Games," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 333-346, February.
    12. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    13. zhao, guo & Chai, Yingming, 2024. "A Sufficient Condition for Weakly Acyclic games with Applications," MPRA Paper 120789, University Library of Munich, Germany.
    14. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:emetrp:v:84:y:2016:i::p:627-676. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.