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<p>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.</p>

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Partially observable discrete-time stochastic games under risk probability criterion

  • 期刊论文

  • 发表日期：

    2025年6月27日

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  • Qingda Wei,
  • Xian Chen

摘要

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.