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Generalized perturbed best response dynamics with a continuum of strategies

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  • Lahkar, Ratul
  • Mukherjee, Sayan
  • Roy, Souvik

Abstract

We consider a generalization of perturbed best response dynamics in population games with a continuum of strategies. The previous literature has considered the logit dynamic generated through the Shannon entropy as a deterministic perturbation. We consider a wider class of deterministic perturbations satisfying lower semicontinuity and strong convexity. Apart from the Shannon entropy, Tsallis entropy and Burg entropy are other perturbations that satisfy these conditions. We thereby generate the generalized perturbed best response dynamic with a continuum of strategies. We establish fundamental properties of the dynamic and show convergence in potential games and negative semidefinite games.

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  • Lahkar, Ratul & Mukherjee, Sayan & Roy, Souvik, 2022. "Generalized perturbed best response dynamics with a continuum of strategies," Journal of Economic Theory, Elsevier, vol. 200(C).
    • Handle: RePEc:eee:jetheo:v:200:y:2022:i:c:s0022053121002155
    DOI: 10.1016/j.jet.2021.105398
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    Cited by:

    1. Lahkar, Ratul & Mukherjee, Sayan & Roy, Souvik, 2023. "The logit dynamic in supermodular games with a continuum of strategies: A deterministic approximation approach," Games and Economic Behavior, Elsevier, vol. 139(C), pages 133-160.
    2. Ratul Lahkar & Sayan Mukherjee & Souvik Roy, 2022. "A Deterministic Approximation Approach to the Continuum Logit Dynamic with an Application to Supermodular Games," Working Papers 79, Ashoka University, Department of Economics.

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    More about this item

    Keywords

    Perturbed best response; Logit dynamic; Potential games; Negative semidefinite games;
    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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