 Zero-sum risk-sensitive stochastic games on a countable state spaceArnab Basu and Mrinal Kanti Ghosh Stochastic Processes and their Applications, 2014, vol. 124, issue 1, 961-983 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. Keywords: Risk-sensitive stochastic games; Exponential discounted and ergodic costs; Shapley equations (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:124:y:2014:i:1:p:961-983 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2013.09.009 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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