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

2016/03/11 by Arnab Basu, Basu, Arnab, Mrinal K. Ghosh +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #91A10 #91A15 #91A25 (Primary) #91A50 (Secondary) #Economic theories and models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Optimization and Control (math.OC) #Stochastic processes and financial applications #math.OC #msc:91A10 #msc:91A15 #msc:91A25 #msc:91A50

paper · pdf · doi:10.48550/arxiv.1603.03683

Submitted on September 16, 2015 for review for possible publication in Mathematics of Operations Research as Manuscript No: MOR-2015-241

arxiv created 2016/03/11 · openalex publication_date 2016/03/11 · arxiv updated 2016/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Discounted linear exponential quadratic Gaussian control

Cited by

• Algorithms for zero-sum stochastic games with the risk-sensitive average criterion

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