Zero-Sum Semi-Markov Games with the Risk-Sensitive Average Reward Criterion

Fang Chen () and Xin Guo ()
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Fang Chen: Peking University
Xin Guo: Sun Yat-Sen University

Journal of Optimization Theory and Applications, 2025, vol. 204, issue 3, No 7, 30 pages

Abstract: Abstract This paper studies the risk-sensitive average reward criterion for the semi-Markov game with compact state and action spaces. Under some suitable conditions (slightly weaker than the existing ones), we introduce a parametric operator, verify that the corresponding spectral radius is an eigenvalue of it by the nonlinear Krein-Rutman theorem, and further show the continuity of the spectral radius in the parameters. By the continuity and the intermediate value property, we prove that the Shapley equation admits a non-trivial solution, and then establish the existence of the value and a stationary saddle point. Furthermore, we present an iteration algorithm for computing (at least approximating) the value of the game. Finally, we give two examples to illustrate our conditions and algorithm.

Keywords: Semi-Markov game; Risk-sensitive average reward criterion; Shapley equation; Compact space; Saddle point; 90C40; 91A15 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-024-02603-2

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