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Partially observable discrete-time stochastic games under risk probability criterion

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  • Qingda Wei

    (Huaqiao University)

  • Xian Chen

    (Xiamen University)

Abstract

This paper studies partially observable discrete-time stochastic games under the risk probability criterion. The observable and unobservable state spaces are Borel spaces and the reward function is nonnegative. We introduce a sequence of probability measures for which the probabilistic interpretation is given. Moreover, we show that the partially observable zero-sum game problem can be solved via introducing a new auxiliary zero-sum game problem with extended state space. The extended state space consists of the observable state space and the joint distribution of the unobservable state and profit level. Furthermore, we establish the value iteration and Shapley equation for the auxiliary zero-sum game problem. Finally, we prove that there exists a saddle-point equilibrium and thus the value of the game exists.

Suggested Citation

  • Qingda Wei & Xian Chen, 2025. "Partially observable discrete-time stochastic games under risk probability criterion," International Journal of Game Theory, Springer;Game Theory Society, vol. 54(2), pages 1-17, December.
    • Handle: RePEc:spr:jogath:v:54:y:2025:i:2:d:10.1007_s00182-025-00951-5
    DOI: 10.1007/s00182-025-00951-5
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    References listed on IDEAS

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    1. Nicole Bäauerle & Ulrich Rieder, 2017. "Partially Observable Risk-Sensitive Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1180-1196, November.
    2. Xiangxiang Huang & Xianping Guo, 2020. "Nonzero-Sum Stochastic Games with Probability Criteria," Dynamic Games and Applications, Springer, vol. 10(2), pages 509-527, June.
    3. M. K. Ghosh & D. McDonald & S. Sinha, 2004. "Zero-Sum Stochastic Games with Partial Information," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 99-118, April.
    4. Subhamay Saha, 2014. "Zero-Sum Stochastic Games with Partial Information and Average Payoff," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 344-354, January.
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