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<p>In this paper, we study two-person zero-sum stochastic games with stopping and control for semi-Markov processes on a Borel state space under a risk-sensitive discounted cost criterion. In this framework, at each decision epoch, both players may either take an action or stop the game. Under suitable assumptions, we deduce that the game has a value obtained as the unique solution of certain dynamic programming inequalities with bilateral constraints. Moreover, we are able to show the existence of a saddle point equilibrium.</p>

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Semi-Markov Stopping Games with Risk-Sensitive Discounted Cost Criterion

  • 期刊论文

  • 发表日期：

    2026年4月17日

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  • Bivakar Bose,
  • Chandan Pal,
  • Subhamay Saha

摘要

In this paper, we study two-person zero-sum stochastic games with stopping and control for semi-Markov processes on a Borel state space under a risk-sensitive discounted cost criterion. In this framework, at each decision epoch, both players may either take an action or stop the game. Under suitable assumptions, we deduce that the game has a value obtained as the unique solution of certain dynamic programming inequalities with bilateral constraints. Moreover, we are able to show the existence of a saddle point equilibrium.