 Best-response dynamics in zero-sum stochastic gamesDavid S. Leslie, Steven Perkins and Zibo Xu Journal of Economic Theory, 2020, vol. 189, issue C Abstract: We define and analyse three learning dynamics for two-player zero-sum discounted-payoff stochastic games. A continuous-time best-response dynamic in mixed strategies is proved to converge to the set of Nash equilibrium stationary strategies. Extending this, we introduce a fictitious-play-like process in a continuous-time embedding of a stochastic zero-sum game, which is again shown to converge to the set of Nash equilibrium strategies. Finally, we present a modified δ-converging best-response dynamic, in which the discount rate converges to 1, and the learned value converges to the asymptotic value of the zero-sum stochastic game. The critical feature of all the dynamic processes is a separation of adaption rates: beliefs about the value of states adapt more slowly than the strategies adapt, and in the case of the δ-converging dynamic the discount rate adapts more slowly than everything else. Keywords: Stochastic games; Best-response dynamics; Zero-sum games; Convergence (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:189:y:2020:i:c:s0022053120300892 DOI: 10.1016/j.jet.2020.105095 Access Statistics for this article Journal of Economic Theory is currently edited by A. Lizzeri and K. Shell More articles in Journal of Economic Theory from Elsevier |
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