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Two-person cooperative uncertain differential game with transferable payoffs

Author

Listed:
  • Yi Zhang

    (Beijing University of Chemical Technology)

  • Jinwu Gao

    (Ocean University of China)

  • Xiang Li

    (Beijing University of Chemical Technology)

  • Xiangfeng Yang

    (University of International Business and Economics)

Abstract

Uncertain differential game models conflicts and interests among players in the context of an uncertain dynamic system. However, cooperative behavior in uncertain differential game is an unexplored terrain. This paper proposes a spectrum of a cooperative uncertain differential game with transferrable payoffs. First, group rationality is achieved by maximizing the coalitional payoff through an uncertain optimal control method. Second, the concept of imputation is introduced as a solution, and a stability condition called subgame consistency condition for an imputation is proposed as well. Furthermore, the derivation of payoff distribution procedure for subgame consistent imputation is discussed. In addition, two optimal principles, i.e., Nash bargaining solution and Shapley value, are extended to this kind of model and are proved to be subgame consistent imputations, and their payoff distribution procedures are derived analytically. Finally, a two-person resource extraction game is studied for illustrating purpose.

Suggested Citation

  • Yi Zhang & Jinwu Gao & Xiang Li & Xiangfeng Yang, 2021. "Two-person cooperative uncertain differential game with transferable payoffs," Fuzzy Optimization and Decision Making, Springer, vol. 20(4), pages 567-594, December.
    • Handle: RePEc:spr:fuzodm:v:20:y:2021:i:4:d:10.1007_s10700-021-09355-y
    DOI: 10.1007/s10700-021-09355-y
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    References listed on IDEAS

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    1. Yun Sun & Yuanguo Zhu, 2017. "Bang–bang property for an uncertain saddle point problem," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 605-613, March.
    2. Petrosjan, Leon & Zaccour, Georges, 2003. "Time-consistent Shapley value allocation of pollution cost reduction," Journal of Economic Dynamics and Control, Elsevier, vol. 27(3), pages 381-398, January.
    3. Liu, Jiaguo & Wang, Junjin, 2019. "Carrier alliance incentive analysis and coordination in a maritime transport chain based on service competition," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 128(C), pages 333-355.
    4. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    5. D. W. K. Yeung & L. A. Petrosyan, 2004. "Subgame Consistent Cooperative Solutions in Stochastic Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 120(3), pages 651-666, March.
    6. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
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    Cited by:

    1. Boyang Dai & Xiangfeng Yang & Xiaoyue Liu, 2022. "Shapley Value of Uncertain Coalitional Game based on Hurwicz Criterion with Application to Water Resource Allocation," Group Decision and Negotiation, Springer, vol. 31(1), pages 241-260, February.
    2. Zijun Li & Fanyong Meng, 2023. "The potential and consistency of the Owen value for fuzzy cooperative games with a coalition structure," Fuzzy Optimization and Decision Making, Springer, vol. 22(3), pages 387-414, September.

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