Zero-sum risk-sensitive stochastic games on a countable state space
Document Type
Article
Publication Title
Stochastic Processes And Their Applications
Abstract
Infinite horizon discounted-cost and ergodic-cost risk-sensitive zero-sum stochastic games for controlled Markov chains with countably many states are analyzed. Upper and lower values for these games are established. The existence of value and saddle-point equilibria in the class of Markov strategies is proved for the discounted-cost game. The existence of value and saddle-point equilibria in the class of stationary strategies is proved under the uniform ergodicity condition for the ergodic-cost game. The value of the ergodic-cost game happens to be the product of the inverse of the risk-sensitivity factor and the logarithm of the common Perron–Frobenius eigenvalue of the associated controlled nonlinear kernels.
Publication Date
1-4-2014
Publisher
Elsevier
Volume
Vol.124
Issue
Iss.1
Recommended Citation
Basu, Arnab and Ghosh, Mrinal Kanti, "Zero-sum risk-sensitive stochastic games on a countable state space" (2014). Faculty Publications. 1773.
https://research.iimb.ac.in/fac_pubs/1773
