Zero-sum risk-sensitive stochastic games on a countable state space

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
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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