Limit Value of Dynamic Zero-Sum Games with Vanishing Stage Duration

• 成果类型: Article
• 署名作者: Sorin, Sylvain
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2017.0851
• 发表日期: 2018
• 页码: 51-63
• 关键词: hamilton-jacobi equations; differential-games; stochastic games; VISCOSITY SOLUTIONS; Asymptotic value; unbounded transition; operator approach; isaacs equations; payoff rates; INFORMATION

摘要

We consider two-person zero-sum games where the players control, at discrete times {t(n)} induced by a partition Pi of R+, a continuous time Markov process. We prove that the limit of the values v(Pi) exist as the mesh of Pi goes to 0. The analysis covers the cases of (1) stochastic games (where both players know the state), and (2) games with unknown state and symmetric signals. The proof is by reduction to deterministic differential games.