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<p>We analyze zero-sum stochastic games for controlled continuous-time Markov decision processes (CTMDPs) over a general state space, employing the risk-sensitive first-passage discounted cost criterion. Both transition and cost rates may be unbounded. Assuming stability, we prove the existence and uniqueness of the solution to the Hamilton-Jacobi-Isaacs (HJI) equation through a value iteration approach. By applying the Feynman-Kac formula, we confirm the presence of a saddle-point equilibrium among Markov strategies, describing it via the associated HJI equation. Lastly, we validate our findings and assumptions with numerical examples.</p>

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Continuous-Time Zero-Sum Games for Markov Decision Processes Under the Risk-Sensitive First Passage Discounted Cost Criterion

  • 期刊论文

  • 发表日期：

    2025年9月29日

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  • Subrata Golui,
  • Jie Xiong

摘要

We analyze zero-sum stochastic games for controlled continuous-time Markov decision processes (CTMDPs) over a general state space, employing the risk-sensitive first-passage discounted cost criterion. Both transition and cost rates may be unbounded. Assuming stability, we prove the existence and uniqueness of the solution to the Hamilton-Jacobi-Isaacs (HJI) equation through a value iteration approach. By applying the Feynman-Kac formula, we confirm the presence of a saddle-point equilibrium among Markov strategies, describing it via the associated HJI equation. Lastly, we validate our findings and assumptions with numerical examples.