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Environmental game modeling with uncertainties

  • * Corresponding author: Shaojian Qu

    * Corresponding author: Shaojian Qu 

The first author is supported by NSSF grant

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  • We model environmental games with stochastic data based on an imprecise distribution which is assumed to be attached to an a-priori known set. Our model is different from previous games where the probability distribution of the uncertain data is precisely given. Our model is also different from the robust games which presents a robust optimization approach to game models with the uncertain data in a compact convex set without probabilistic information which can lead to overly conservative solutions. A distributionally robust approach is used to cope with our setting in the games by combining the stochastic optimization and robust optimization approaches which can be termed as the distributionally robust environmental games. We show that the existence of an equilibrium for the distributionally robust environmental games under mild assumptions. The computation method for equilibrium, with the first- and second-information about the probability of uncertain data, can be reformulated as a semidefinite programming problem which can be tractably realized. Numerical tests are given to show the efficiency of the proposed methods.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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  • Table 1.  Numerical results for the robustness of our method

    $\delta$ NSCW CSCW USCW
    TSC 0 2.0001 2.446 1.2269
    TASC 0 1.8 2.1333 1.8
    TS 0.01 2 2.4456 2
    TASC 0.01 1.801 2.1565 1.801
    TSC 0.03 1.9981 2.4448 1.9981
    TASC 0.03 1.803 2.1602 1.803
    TSC 0.05 1.9906 2.444 1.9906
    TASC 0.05 1.805 2.1625 1.805
    TSC 0.1 1.9811 2.4421 1.9811
    TASC 0.1 1.8155 2.1681 1.8155
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