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Discrete-time stopping games with risk-sensitive discounted cost criterion

Author

Listed:
  • Wenzhao Zhang

    (Fuzhou University
    Center for Applied Mathematics of Fujian Province)

  • Congying Liu

    (Fuzhou University)

Abstract

In this paper, we focus on the discrete-time stopping games under the risk-sensitive discounted cost criterion. The state space and the action spaces of all the players are assumed to be Borel spaces. The cost functions are allowed to be unbounded from above and from below. At each decision epoch, each player chooses an action to influence the transition laws, and player 1 incurs a running cost. If players 1 or 2 decides to stop the game, player 1 incurs a corresponding terminated cost. Under suitable hypothesis, we show that the game model has a value which is a unique solution of risk-sensitive stopping optimality equation by an approximation technique. Furthermore, we derive the existence of equilibria.

Suggested Citation

  • Wenzhao Zhang & Congying Liu, 2024. "Discrete-time stopping games with risk-sensitive discounted cost criterion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(2), pages 437-466, October.
    • Handle: RePEc:spr:mathme:v:100:y:2024:i:2:d:10.1007_s00186-024-00864-1
    DOI: 10.1007/s00186-024-00864-1
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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.
    2. Qingda Wei & Xian Chen, 2021. "Nonzero-sum Risk-Sensitive Average Stochastic Games: The Case of Unbounded Costs," Dynamic Games and Applications, Springer, vol. 11(4), pages 835-862, December.
    3. Bäuerle, Nicole & Rieder, Ulrich, 2017. "Zero-sum risk-sensitive stochastic games," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 622-642.
    4. Xiangxiang Huang & Xianping Guo, 2020. "Nonzero-Sum Stochastic Games with Probability Criteria," Dynamic Games and Applications, Springer, vol. 10(2), pages 509-527, June.
    5. Rolando Cavazos-Cadena & Mario Cantú-Sifuentes & Imelda Cerda-Delgado, 2021. "Nash equilibria in a class of Markov stopping games with total reward criterion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(2), pages 319-340, October.
    6. Arnab Basu & Mrinal K. Ghosh, 2018. "Nonzero-Sum Risk-Sensitive Stochastic Games on a Countable State Space," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 516-532, May.
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