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Risk-Sensitive Average Equilibria for Discrete-Time Stochastic Games

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  • Qingda Wei

    (Huaqiao University)

  • Xian Chen

    (Xiamen University)

Abstract

In this paper, we study the risk-sensitive average payoff criterion for the nonzero-sum discrete-time stochastic games with a denumerable state space. The risk-sensitivity coefficient can take positive values and negative values. Under the suitable conditions, we show the existence of a solution to the coupled equations by a technique of the discounted approximation, and obtain the existence of a stationary Nash equilibrium. Moreover, we present some verifiable sufficient conditions imposed on the primitive data of the model for the verification of our assumption and use an example to illustrate that our conditions are weaker than those in the existing literature.

Suggested Citation

  • Qingda Wei & Xian Chen, 2019. "Risk-Sensitive Average Equilibria for Discrete-Time Stochastic Games," Dynamic Games and Applications, Springer, vol. 9(2), pages 521-549, June.
    • Handle: RePEc:spr:dyngam:v:9:y:2019:i:2:d:10.1007_s13235-018-0267-5
    DOI: 10.1007/s13235-018-0267-5
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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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    4. Rolando Cavazos-Cadena & Daniel Hernández-Hernández, 2011. "Discounted Approximations for Risk-Sensitive Average Criteria in Markov Decision Chains with Finite State Space," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 133-146, February.
    5. Bäuerle, Nicole & Rieder, Ulrich, 2017. "Zero-sum risk-sensitive stochastic games," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 622-642.
    6. Ronald A. Howard & James E. Matheson, 1972. "Risk-Sensitive Markov Decision Processes," Management Science, INFORMS, vol. 18(7), pages 356-369, March.
    7. Andrzej Nowak, 2007. "On stochastic games in economics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 513-530, December.
    8. 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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    Cited by:

    1. Elena Parilina & Stepan Akimochkin, 2021. "Cooperative Stochastic Games with Mean-Variance Preferences," Mathematics, MDPI, vol. 9(3), pages 1-15, January.
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    3. 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.

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