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Generalized Perturbed Best Response Dynamics with a Continuum of Strategies

Author

Listed:
  • RatulLahkar

    (Department of Economics, Ashoka UniversityAuthor-Name:)

  • Sayan Mukherjee

    (Indian Statistical Institute, Kolkata)

  • Souvik Roy

    (Indian Statistical Institute, Kolkata)

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.

Suggested Citation

  • RatulLahkar & Sayan Mukherjee & Souvik Roy, 2021. "Generalized Perturbed Best Response Dynamics with a Continuum of Strategies," Working Papers 51, Ashoka University, Department of Economics.
    • Handle: RePEc:ash:wpaper:51
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    References listed on IDEAS

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    1. Jakub Bielawski & Thiparat Chotibut & Fryderyk Falniowski & Michal Misiurewicz & Georgios Piliouras, 2022. "Unpredictable dynamics in congestion games: memory loss can prevent chaos," Papers 2201.10992, arXiv.org, revised Jan 2022.

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