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Risk-sensitive continuous-time stochastic games with the average criterion and a compact state space

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  • Guo, Xin
  • Zheng, Zewu

Abstract

This paper attempts to study the risk-sensitive average continuous-time stochastic game with compact state and action spaces. We derive an equivalent Shapley equation for the risk-sensitive average criterion. By building a novel parametric operator and analyzing the properties of an eigenvalue of the operator, we prove the equivalent Shapley equation admits a solution, and then establish the existence of the value and a Nash equilibrium over the class of history-dependent policies. Moreover, we design an iterative algorithm for computing the value of the game and prove the convergence of the algorithm. Finally, two examples are given to verify our results.

Suggested Citation

  • Guo, Xin & Zheng, Zewu, 2025. "Risk-sensitive continuous-time stochastic games with the average criterion and a compact state space," Stochastic Processes and their Applications, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:spapps:v:188:y:2025:i:c:s0304414925001292
    DOI: 10.1016/j.spa.2025.104688
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    References listed on IDEAS

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    1. Basu, Arnab & Ghosh, Mrinal Kanti, 2014. "Zero-sum risk-sensitive stochastic games on a countable state space," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 961-983.
    2. Ghosh, Mrinal K. & Golui, Subrata & Pal, Chandan & Pradhan, Somnath, 2023. "Discrete-time zero-sum games for Markov chains with risk-sensitive average cost criterion," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 40-74.
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    4. Wei, Qingda, 2019. "Nonzero-sum risk-sensitive finite-horizon continuous-time stochastic games," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 96-104.
    5. Bäuerle, Nicole & Rieder, Ulrich, 2017. "Zero-sum risk-sensitive stochastic games," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 622-642.
    6. Xianping Guo & Alexei Piunovskiy, 2011. "Discounted Continuous-Time Markov Decision Processes with Constraints: Unbounded Transition and Loss Rates," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 105-132, February.
    7. Subrata Golui & Chandan Pal & Subhamay Saha, 2022. "Continuous-Time Zero-Sum Games for Markov Decision Processes with Discounted Risk-Sensitive Cost Criterion," Dynamic Games and Applications, Springer, vol. 12(2), pages 485-512, June.
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