Nonzero-Sum Risk-Sensitive Stochastic Games on a Countable State Space

• 成果类型: Article
• 署名作者: Basu, Arnab; Ghosh, Mrinal K.
• 署名单位: Indian Institute of Management (IIM System); Indian Institute of Management Bangalore; Indian Institute of Science (IISC) - Bangalore
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2017.0870
• 发表日期: 2018
• 页码: 516-532
• 关键词: markov decision chains; quadratic-gaussian control; infinite-horizon risk; differential-games; Nash equilibria; optimal strategies; dynamic-games; optimality; average; ergodicity

摘要

The infinite horizon risk-sensitive discounted-cost and ergodic-cost nonzero-sum stochastic games for controlled Markov chains with countably many states are analyzed. For the discounted-cost game, we prove the existence of Nash equilibrium strategies in the class of Markov strategies under fairly general conditions. Under an additional weak geometric ergodicity condition and a small cost criterion, the existence of Nash equilibrium strategies in the class of stationary Markov strategies is proved for the ergodic-cost game. The key nontrivial contributions in the ergodic part are to prove the existence of a particular form of a (relative) value function solution to a player's Bellman equation and the continuity of this solution with respect to the opponent's strategies.