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Nonzero-sum risk-sensitive finite-horizon continuous-time stochastic games

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  • Wei, Qingda

Abstract

This paper concerns the nonzero-sum games for continuous-time jump processes with unbounded transition rates under the risk-sensitive finite-horizon cost criterion. The state space is a countable set and the costs are allowed to be unbounded in the game model. Under the suitable optimality conditions, by introducing an appropriate topology for the set of all randomized Markov multi-strategies and employing the risk-sensitive finite-horizon optimality equations of the players, we prove the existence of a randomized Markov Nash equilibrium in the class of all randomized history-dependent multi-strategies.

Suggested Citation

  • Wei, Qingda, 2019. "Nonzero-sum risk-sensitive finite-horizon continuous-time stochastic games," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 96-104.
    • Handle: RePEc:eee:stapro:v:147:y:2019:i:c:p:96-104
    DOI: 10.1016/j.spl.2018.12.004
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    References listed on IDEAS

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    1. Qingda Wei, 2016. "Continuous-time Markov decision processes with risk-sensitive finite-horizon cost criterion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(3), pages 461-487, December.
    2. V. Rykov & M. Yu. Kitaev, 1995. "Controlled queueing systems," International Journal of Stochastic Analysis, Hindawi, vol. 8, pages 1-3, January.
    3. Elżbieta Ferenstein, 2007. "Randomized stopping games and Markov market games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 531-544, December.
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    Cited by:

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    2. Chen, Fang & Guo, Xianping, 2023. "Two-person zero-sum risk-sensitive stochastic games with incomplete reward information on one side," Stochastic Processes and their Applications, Elsevier, vol. 165(C), pages 218-245.

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