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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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    References listed on IDEAS

    as
    1. Perkins, S. & Leslie, D.S., 2014. "Stochastic fictitious play with continuous action sets," Journal of Economic Theory, Elsevier, vol. 152(C), pages 179-213.
    2. Martin Posch, 1997. "Cycling in a stochastic learning algorithm for normal form games," Journal of Evolutionary Economics, Springer, vol. 7(2), pages 193-207.
    3. , P. & , Peyton, 2006. "Regret testing: learning to play Nash equilibrium without knowing you have an opponent," Theoretical Economics, Econometric Society, vol. 1(3), pages 341-367, September.
    4. Steffen Huck & Hans-Theo Normann & Joerg Oechssler, 2004. "Through Trial and Error to Collusion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(1), pages 205-224, February.
    5. Germano, Fabrizio & Lugosi, Gabor, 2007. "Global Nash convergence of Foster and Young's regret testing," Games and Economic Behavior, Elsevier, vol. 60(1), pages 135-154, July.
    6. Michel Benaim & Mathieu Faure, 2010. "Stochastic Approximation, Cooperative Dynamics and Supermodular Games," Levine's Working Paper Archive 814577000000000437, David K. Levine.
    7. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    8. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2005. "Stochastic Approximations and Differential Inclusions; Part II: Applications," Working Papers hal-00242974, HAL.
    9. Dindos, Martin & Mezzetti, Claudio, 2006. "Better-reply dynamics and global convergence to Nash equilibrium in aggregative games," Games and Economic Behavior, Elsevier, vol. 54(2), pages 261-292, February.
    10. Babichenko, Yakov, 2012. "Completely uncoupled dynamics and Nash equilibria," Games and Economic Behavior, Elsevier, vol. 76(1), pages 1-14.
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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).
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    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.

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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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