Markov Games with Frequent Actions and Incomplete Information-The Limit Case

• 成果类型: Article
• 署名作者: Cardaliaguet, Pierre; Rainer, Catherine; Rosenberg, Dinah; Vieille, Nicolas
• 署名单位: Universite PSL; Universite Paris-Dauphine; Universite de Bretagne Occidentale; Hautes Etudes Commerciales (HEC) Paris
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2015.0715
• 发表日期: 2016
• 页码: 49-71
• 关键词: Stochastic games; obstacle problem

摘要

We study the asymptotics of a class of two-player, zero-sum stochastic game with incomplete information on one side when the time span between two consecutive stages vanishes. The informed player observes the realization of a Markov chain on which the payoffs depend, whereas the noninformed player only observes his opponent's actions. We show the existence of a limit value; this value is characterized through an auxiliary optimization problem and as the solution of a Hamilton-Jacobi equation.