Nonzero-Sum Risk-Sensitive Stochastic Games on a Countable State Space

Basu, Arnab and Ghosh, Mrinal K (2018) Nonzero-Sum Risk-Sensitive Stochastic Games on a Countable State Space. In: MATHEMATICS OF OPERATIONS RESEARCH, 43 (2). pp. 516-532.

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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.

Item Type:	Journal Article
Publication:	MATHEMATICS OF OPERATIONS RESEARCH
Publisher:	INFORMS, 5521 RESEARCH PARK DR, SUITE 200, CATONSVILLE, MD 21228 USA
Additional Information:	Copy right for this article belong to INFORMS, 5521 RESEARCH PARK DR, SUITE 200, CATONSVILLE, MD 21228 USA
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	30 Aug 2018 15:41
Last Modified:	30 Aug 2018 15:41
URI:	http://eprints.iisc.ac.in/id/eprint/60536

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