Generalized perturbed best response dynamics with a continuum of strategies

• 成果类型: Article
• 署名作者: Lahkar, Ratul; Mukherjee, Sayan; Roy, Souvik
• 署名单位: Ashoka University; Indian Statistical Institute; Indian Statistical Institute Kolkata
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2021.105398
• 发表日期: 2022
• 关键词: Perturbed best response; Logit dynamic; potential games; Negative semidefinite games

摘要

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. (c) 2021 Elsevier Inc. All rights reserved.