Nonzero-sum Risk-sensitive Stochastic Games on a Countable State Space
Optimization and Control
2016-03-14 v1
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 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.
Keywords
Cite
@article{arxiv.1603.03683,
title = {Nonzero-sum Risk-sensitive Stochastic Games on a Countable State Space},
author = {Arnab Basu and Mrinal K. Ghosh},
journal= {arXiv preprint arXiv:1603.03683},
year = {2016}
}
Comments
Submitted on September 16, 2015 for review for possible publication in Mathematics of Operations Research as Manuscript No: MOR-2015-241