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arXiv · 1603.03683

Nonzero-sum Risk-sensitive Stochastic Games on a Countable State Space

Arnab Basu·Mrinal K. Ghosh
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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 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.

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Arnab Basu, Mrinal K. Ghosh. 2016-03-11. Nonzero-sum Risk-sensitive Stochastic Games on a Countable State Space. https://arxiv.org/abs/1603.03683

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