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Continuous-Time Zero-Sum Games for Markov Decision Processes with Discounted Risk-Sensitive Cost Criterion

Author

Listed:
  • Subrata Golui

    (Indian Institute of Technology Guwahati)

  • Chandan Pal

    (Indian Institute of Technology Guwahati)

  • Subhamay Saha

    (Indian Institute of Technology Guwahati)

Abstract

In this paper, we study two-person zero-sum stochastic games for controlled continuous time Markov decision processes with risk-sensitive discounted cost criterion. The transition and cost rates are possibly unbounded. For the zero-sum stochastic game, we prove the existence of the value of the game and saddle-point equilibrium in the class of history dependent strategies under a Foster–Lyapunov condition. We achieve our results by studying the corresponding Hamilton–Jacobi–Isaacs equation.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:dyngam:v:12:y:2022:i:2:d:10.1007_s13235-021-00391-2
    DOI: 10.1007/s13235-021-00391-2
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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.
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