Nonzero-Sum Stochastic Games with Probability Criteria

Xiangxiang Huang () and Xianping Guo ()
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Xiangxiang Huang: Dongguan University of Technology
Xianping Guo: Sun Yat-Sen University

Dynamic Games and Applications, 2020, vol. 10, issue 2, No 9, 509-527

Abstract: 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.

Keywords: Nonzero-sum discrete-time stochastic game; Probability criterion; Nash equilibrium; An application; 91A05; 91A25 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13235-019-00317-z

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