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Best-response dynamics, playing sequences, and convergence to equilibrium in random games

Author

Listed:
  • Torsten Heinrich

    (Chemnitz University of Technology
    University of Oxford
    University of Oxford)

  • Yoojin Jang

    (University of Oxford
    University of Oxford)

  • Luca Mungo

    (University of Oxford
    University of Oxford)

  • Marco Pangallo

    (CENTAI Institute)

  • Alex Scott

    (University of Oxford)

  • Bassel Tarbush

    (University of Oxford)

  • Samuel Wiese

    (University of Oxford
    University of Oxford)

Abstract

We analyze the performance of the best-response dynamic across all normal-form games using a random games approach. The playing sequence—the order in which players update their actions—is essentially irrelevant in determining whether the dynamic converges to a Nash equilibrium in certain classes of games (e.g. in potential games) but, when evaluated across all possible games, convergence to equilibrium depends on the playing sequence in an extreme way. Our main asymptotic result shows that the best-response dynamic converges to a pure Nash equilibrium in a vanishingly small fraction of all (large) games when players take turns according to a fixed cyclic order. By contrast, when the playing sequence is random, the dynamic converges to a pure Nash equilibrium if one exists in almost all (large) games.

Suggested Citation

  • Torsten Heinrich & Yoojin Jang & Luca Mungo & Marco Pangallo & Alex Scott & Bassel Tarbush & Samuel Wiese, 2023. "Best-response dynamics, playing sequences, and convergence to equilibrium in random games," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 703-735, September.
    • Handle: RePEc:spr:jogath:v:52:y:2023:i:3:d:10.1007_s00182-023-00837-4
    DOI: 10.1007/s00182-023-00837-4
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    References listed on IDEAS

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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 Oct 2024.
    2. Andrea Collevecchio & Hlafo Alfie Mimun & Matteo Quattropani & Marco Scarsini, 2024. "Basins of Attraction in Two-Player Random Ordinal Potential Games," Papers 2407.05460, arXiv.org, revised Feb 2025.
    3. Zi Wang & Xingcheng Xu & Yanqing Yang & Xiaodong Zhu, 2024. "Optimal Trade and Industrial Policies in the Global Economy: A Deep Learning Framework," Working Papers tecipa-781, University of Toronto, Department of Economics.
    4. Mimun, Hlafo Alfie & Quattropani, Matteo & Scarsini, Marco, 2024. "Best-response dynamics in two-person random games with correlated payoffs," Games and Economic Behavior, Elsevier, vol. 145(C), pages 239-262.
    5. Andrea Collevecchio & Tuan-Minh Nguyen & Ziwen Zhong, 2024. "Finding pure Nash equilibria in large random games," Papers 2406.09732, arXiv.org, revised Aug 2024.
    6. zhao, guo & Chai, Yingming, 2024. "A Sufficient Condition for Weakly Acyclic games with Applications," MPRA Paper 120789, University Library of Munich, Germany.

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    More about this item

    Keywords

    Best-response dynamics; Equilibrium convergence; Random games;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • 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
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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