Zero-Sum Stopping Games with Asymmetric Information

• 成果类型: Article
• 署名作者: Gensbittel, Fabien; Grun, Christine
• 署名单位: Universite de Toulouse; Universite Toulouse 1 Capitole; Toulouse School of Economics
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2017.0924
• 发表日期: 2019
• 页码: 277-302
• 关键词: stochastic differential-games; markov-chain games; incomplete information; continuous-time; optimal strategies; dynkin games; limit

摘要

We study a model of two-player, zero-sum, stopping games with asymmetric information. We assume that the payoff depends on two independent continuous-time Markov chains, where the first Markov chain is only observed by player 1 and the second Markov chain is only observed by player 2, implying that the players have access to stopping times with respect to different filtrations. We show the existence of a value in mixed stopping times and provide a variational characterization for the value as a function of the initial distribution of the Markov chains. We also prove a verification theorem for optimal stopping rules, which allows to construct optimal stopping times. Finally we use our results to solve explicitly two generic examples.