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Learning with minimal information in continuous games

Author

Listed:
  • Bervoets, Sebastian

    (Aix-Marseille Univ., CNRS, EHESS, Centrale Marseille, AMSE, Marseille, France)

  • Bravo, Mario

    (Universidad de Santiago de Chile, Departamento de Matem\'atica y Ciencia de la Computaci\'on)

  • Faure, Mathieu

    (Aix-Marseille Univ., CNRS, EHESS, Centrale Marseille, AMSE, Marseille, France)

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

  • Bervoets, Sebastian & Bravo, Mario & Faure, Mathieu, 2020. "Learning with minimal information in continuous games," Theoretical Economics, Econometric Society, vol. 15(4), November.
    • Handle: RePEc:the:publsh:3435
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    References listed on IDEAS

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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. Péter Bayer & György Kozics & Nóra Gabriella Szőke, 2020. "Best-Response Dynamics in Directed Network Games," CEU Working Papers 2020_1, Department of Economics, Central European University.
    3. P'eter Bayer & Gyorgy Kozics & N'ora Gabriella SzH{o}ke, 2021. "Best-response dynamics in directed network games," Papers 2101.03863, arXiv.org.

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    More about this item

    Keywords

    Payoff-based learning; continuous games; stochastic approximation;
    All these keywords.

    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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