Nonzero-sum risk-sensitive stochastic games on a countable state space
Document Type
Article
Publication Title
Mathematics of Operations Research
Abstract
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.
DOI Link
Publication Date
31-10-2017
Publisher
Informs (Institute for Operations Research and The Management Sciences)
Volume
Vol.43
Issue
Iss.2
Recommended Citation
Basu, Arnab and Ghosh, Mrinal K, "Nonzero-sum risk-sensitive stochastic games on a countable state space" (2017). Faculty Publications. 536.
https://research.iimb.ac.in/fac_pubs/536
