Absorption paths and equilibria in quitting games

• 成果类型: Article
• 署名作者: Ashkenazi-Golan, Galit; Krasikov, Ilia; Rainer, Catherine; Solan, Eilon
• 署名单位: University of London; London School Economics & Political Science; HSE University (National Research University Higher School of Economics); Centre National de la Recherche Scientifique (CNRS); Universite de Bretagne Occidentale
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-022-01807-6
• 发表日期: 2024
• 页码: 735-762
• 关键词: 2-player stochastic games

摘要

We study quitting games and introduce an alternative notion of strategy profiles- absorption paths. An absorption path is parametrized by the total probability of absorption in past play rather than by time, and it accommodates both discrete-time aspects and continuous-time aspects. We then define the concept of sequentially 0-pelfect absorption paths, which are shown to be limits of epsilon-equilibrium strategy profiles as epsilon goes to 0. We establish that all quitting games that do not have simple equilibria (that is, an equilibrium where the game terminates in the first period or one where the game never terminates) have a sequentially 0-perfect absorption path. Finally, we prove the existence of sequentially 0-perfect absorption paths in a new class of quitting games.