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Looking Forward Approach in Cooperative Differential Games with Uncertain Stochastic Dynamics

Author

Listed:
  • Ovanes Petrosian

    (Saint-Petersburg State University)

  • Andrey Barabanov

    (Saint-Petersburg State University)

Abstract

In this study, a novel approach for defining and computing a solution for a differential game is presented for a case, wherein players do not have complete information about the game structure for the full time interval. At any instant in time, players have certain information about the motion equations and payoff functions for a current subinterval, and a forecast about the game structure for the rest of the time interval. The forecast is described by stochastic differential equations. The information about the game structure updates at fixed instants of time and is completely unknown in advance. A new solution is defined as a recursive combination of sets of imputations in the combined truncated subgames that are analyzed by the Looking Forward Approach. An example with a resource extraction game is presented to demonstrate a comparison of payoff functions without a forecast and that with stochastic and deterministic forecasts.

Suggested Citation

  • Ovanes Petrosian & Andrey Barabanov, 2017. "Looking Forward Approach in Cooperative Differential Games with Uncertain Stochastic Dynamics," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 328-347, January.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:1:d:10.1007_s10957-016-1009-8
    DOI: 10.1007/s10957-016-1009-8
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    References listed on IDEAS

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    1. S. Jørgensen & G. Martín-Herrán & G. Zaccour, 2003. "Agreeability and Time Consistency in Linear-State Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 49-63, October.
    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.
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    Cited by:

    1. Jiangjing Zhou & Anna Tur & Ovanes Petrosian & Hongwei Gao, 2021. "Transferable Utility Cooperative Differential Games with Continuous Updating Using Pontryagin Maximum Principle," Mathematics, MDPI, vol. 9(2), pages 1-22, January.
    2. Ovanes Petrosian, 2018. "About the Looking Forward Approach in Cooperative Differential Games with Transferable Utility," HSE Working papers WP BRP 183/EC/2018, National Research University Higher School of Economics.
    3. Ovanes Petrosian & Lihong Shi & Yin Li & Hongwei Gao, 2019. "Moving Information Horizon Approach for Dynamic Game Models," Mathematics, MDPI, vol. 7(12), pages 1-31, December.
    4. David Yeung & Ovanes Petrosian, 2017. "Infinite Horizon Dynamic Games: A New Approach via Information Updating," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-23, December.

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