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Nonzero-Sum Stochastic Games with Probability Criteria

Author

Listed:
  • Xiangxiang Huang

    (Dongguan University of Technology)

  • Xianping Guo

    (Sun Yat-Sen University)

Abstract

In this paper, we consider two-person nonzero-sum discrete-time stochastic games under the probability criterion. Taking $$\lambda $$λ for player 1 and $$\mu $$μ for player 2 as their profit goal, the two players are concerned with the probabilities that the rewards they earn before the first passage to some target state set are more than $$\lambda $$λ and $$\mu $$μ, respectively. We firstly give a characterization of the probabilities, and then, under a mild condition, we show that the optimal value function for each player is the unique solution to the corresponding optimality equation by an iterative approximation, and then establish the existence of Nash equilibria. Finally, a queueing system is provided to show the application of our main result.

Suggested Citation

  • Xiangxiang Huang & Xianping Guo, 2020. "Nonzero-Sum Stochastic Games with Probability Criteria," Dynamic Games and Applications, Springer, vol. 10(2), pages 509-527, June.
    • Handle: RePEc:spr:dyngam:v:10:y:2020:i:2:d:10.1007_s13235-019-00317-z
    DOI: 10.1007/s13235-019-00317-z
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    References listed on IDEAS

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    1. Yonghui Huang & Xianping Guo & Xinyuan Song, 2011. "Performance Analysis for Controlled Semi-Markov Systems with Application to Maintenance," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 395-415, August.
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    Cited by:

    1. Cao, Haoyang & Guo, Xin, 2022. "MFGs for partially reversible investment," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 995-1014.

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