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

Ghosh, MK and Golui, S and Pal, C and Pradhan, S (2023) Discrete-time zero-sum games for Markov chains with risk-sensitive average cost criterion. In: Stochastic Processes and their Applications, 158 . pp. 40-74.

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Official URL: https://doi.org/10.1016/j.spa.2022.12.009


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. © 2022 Elsevier B.V.

Item Type: Journal Article
Publication: Stochastic Processes and their Applications
Publisher: Elsevier B.V.
Additional Information: The copyright for this article belongs to the Authors.
Keywords: Game theory; Markov processes; Stochastic systems, Average-cost criteria; History dependent strategy; Risk-sensitive average cost criteria; Risk-sensitive zero-sum game; Saddle-point equilibriums; Shapley; Shapley equation; State-space; Value functions; Zero-sum game, Eigenvalues and eigenfunctions
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 02 Feb 2023 10:00
Last Modified: 02 Feb 2023 10:00
URI: https://eprints.iisc.ac.in/id/eprint/79769

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