Discrete-time zero-sum games for Markov chains with risk-sensitive average cost criterion

Mrinal K. Ghosh, Subrata Golui, Chandan Pal and Somnath Pradhan

Stochastic Processes and their Applications, 2023, vol. 158, issue C, 40-74

Abstract: We study zero-sum stochastic games for controlled discrete time Markov chains with risk-sensitive average cost criterion with countable/compact state space and Borel action spaces. The payoff function is nonnegative and possibly unbounded for countable state space case and for compact state space case it is a real-valued and bounded function. For countable state space case, under a certain Lyapunov type stability assumption on the dynamics we establish the existence of the value and a saddle point equilibrium. For compact state space case we establish these results without any Lyapunov type stability assumptions. Using the stochastic representation of the principal eigenfunction of the associated optimality equation, we completely characterize all possible saddle point strategies in the class of stationary Markov strategies. Also, we present and analyze an illustrative example.

Keywords: Risk-sensitive zero-sum game; Risk-sensitive average cost criterion; History dependent strategies; Shapley equations; Value function; Saddle point equilibrium (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:158:y:2023:i:c:p:40-74

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DOI: 10.1016/j.spa.2022.12.009

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