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Learning with minimal information in continuous games

Author

Listed:
  • Sebastian Bervoets

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Mario Bravo

    (USACH - Universidad de Santiago de Chile [Santiago])

  • Mathieu Faure

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

While payoff-based learning models are almost exclusively devised for finite action games, where players can test every action, it is harder to design such learning processes for continuous games. We construct a stochastic learning rule, designed for games with continuous action sets, which requires no sophistication from the players and is simple to implement: players update their actions according to variations in own payoff between current and previous action. We then analyze its behavior in several classes of continuous games and show that convergence to a stable Nash equilibrium is guaranteed in all games with strategic complements as well as in concave games, while convergence to Nash occurs in all locally ordinal potential games as soon as Nash equilibria are isolated.

Suggested Citation

  • Sebastian Bervoets & Mario Bravo & Mathieu Faure, 2020. "Learning with minimal information in continuous games," Post-Print hal-02534257, HAL.
    • Handle: RePEc:hal:journl:hal-02534257
    DOI: 10.3982/TE3435
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    Cited by:

    1. Bayer, Péter & Herings, P. Jean-Jacques & Peeters, Ronald, 2021. "Farsighted manipulation and exploitation in networks," Journal of Economic Theory, Elsevier, vol. 196(C).
    2. Daniele Cassese & Paolo Pin, 2025. "Decentralized pure exchange processes on networks," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 64(3), pages 427-463, May.
    3. Bayer, Péter & Kozics, György & Szőke, Nóra Gabriella, 2023. "Best-response dynamics in directed network games," Journal of Economic Theory, Elsevier, vol. 213(C).
    4. P'eter Bayer & Gyorgy Kozics & N'ora Gabriella SzH{o}ke, 2021. "Best-response dynamics in directed network games," Papers 2101.03863, arXiv.org.

    More about this item

    Keywords

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    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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