Basu, Arnab and Ghosh, Mrinal Kanti (2014) Zero-sum risk-sensitive stochastic games on a countable state space. In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 124 (1). pp. 961-983.
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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. (C) 2013 Elsevier B.V. All rights reserved.
Item Type: | Journal Article |
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Publication: | STOCHASTIC PROCESSES AND THEIR APPLICATIONS |
Publisher: | ELSEVIER SCIENCE BV |
Additional Information: | Copyright for this article belongs to the ELSEVIER SCIENCE BV,NETHERLANDS |
Keywords: | Risk-sensitive stochastic games; Exponential discounted and ergodic costs; Shapley equations |
Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
Date Deposited: | 13 Feb 2014 12:03 |
Last Modified: | 13 Feb 2014 12:03 |
URI: | http://eprints.iisc.ac.in/id/eprint/48374 |
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