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Adaptive learning and p-best response sets

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  • J. Durieu
  • P. Solal
  • O. Tercieux

Abstract

A product set of strategies is a p-best response set if for each agent it contains all best responses to any distribution placing at least probability p on his opponents' profiles belonging to the product set. A p-best response set is minimal if it does not properly contain another p-best response set. We study a perturbed joint fictitious play process with bounded memory and sample and a perturbed independent fictitious play process as in Young (Econometrica 61:57-84, ). We show that in n-person games only strategies contained in the unique minimal p-best response set can be selected in the long run by both types of processes provided that the rate of perturbations and p are sufficiently low. For each process, an explicit bound of p is given and we analyze how this critical value evolves when n increases. Our results are robust to the degree of incompleteness of sampling relative to memory.
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Suggested Citation

  • J. Durieu & P. Solal & O. Tercieux, 2011. "Adaptive learning and p-best response sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 735-747, November.
    • Handle: RePEc:spr:jogath:v:40:y:2011:i:4:p:735-747
    DOI: 10.1007/s00182-010-0266-2
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    Cited by:

    1. P. Jean-Jacques Herings & Andrey Meshalkin & Arkadi Predtetchinski, 2020. "Optimality, Equilibrium, and Curb Sets in Decision Problems Without Commitment," Dynamic Games and Applications, Springer, vol. 10(2), pages 478-492, June.
    2. Desgranges, Gabriel & Gauthier, Stéphane, 2016. "Rationalizability and efficiency in an asymmetric Cournot oligopoly," International Journal of Industrial Organization, Elsevier, vol. 44(C), pages 163-176.
    3. Jacques Durieu & Philippe Solal, 2012. "Models of Adaptive Learning in Game Theory," Chapters, in: Richard Arena & Agnès Festré & Nathalie Lazaric (ed.), Handbook of Knowledge and Economics, chapter 11, Edward Elgar Publishing.
    4. Barthel, Anne-Christine & Hoffmann, Eric & Sabarwal, Tarun, 2022. "Characterizing robust solutions in monotone games," Games and Economic Behavior, Elsevier, vol. 135(C), pages 201-219.
    5. Anne-Christine Barthel & Eric Hoffmann & Tarun Sabarwal, 2021. "A Unified Approach to p-Dominance and its Generalizations in Games with Strategic Complements and Substitutes," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202109, University of Kansas, Department of Economics.
    6. Maruta, Toshimasa & Okada, Akira, 2012. "Stochastically stable equilibria in n-person binary coordination games," Mathematical Social Sciences, Elsevier, vol. 63(1), pages 31-42.
    7. J. Durieu & P. Solal, 2014. "Local Interactions and p -Best Response Set," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-7, March.

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    More about this item

    Keywords

    Evolutionary game theory; Fictitious play process; p-Dominance; Stochastic stability; C72; C73;
    All these keywords.

    JEL classification:

    • 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

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