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Non-Renewable Resource Extraction Model with Uncertainties

Author

Listed:
  • Peichen Ye

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia)

  • Anna Tur

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia)

  • Yilun Wu

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia)

Abstract

This paper delves into a multi-player non-renewable resource extraction differential game model, where the duration of the game is a random variable with a composite distribution function. We first explore the conditions under which the cooperative solution also constitutes a Nash equilibrium, thereby extending the theoretical framework from a fixed duration to the more complex and realistic setting of random duration. Assuming that players are unaware of the switching moment of the distribution function, we derive optimal estimates in both time-dependent and state-dependent cases. The findings contribute to a deeper understanding of strategic decision-making in resource extraction under uncertainty and have implications for various fields where random durations and cooperative strategies are relevant.

Suggested Citation

  • Peichen Ye & Anna Tur & Yilun Wu, 2025. "Non-Renewable Resource Extraction Model with Uncertainties," Games, MDPI, vol. 16(5), pages 1-23, October.
    • Handle: RePEc:gam:jgames:v:16:y:2025:i:5:p:52-:d:1766967
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    References listed on IDEAS

    as
    1. Ekaterina Viktorovna Gromova & José Daniel López-Barrientos, 2016. "A Differential Game Model for The Extraction of Nonrenewable Resources with Random Initial Times — The Cooperative and Competitive Cases," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-19, June.
    2. Anastasiia Zaremba & Ekaterina Gromova & Anna Tur, 2020. "A Differential Game with Random Time Horizon and Discontinuous Distribution," Mathematics, MDPI, vol. 8(12), pages 1-21, December.
    3. Tatyana Balas & Anna Tur, 2023. "The Hamilton–Jacobi–Bellman Equation for Differential Games with Composite Distribution of Random Time Horizon," Mathematics, MDPI, vol. 11(2), pages 1-13, January.
    4. Frederick Ploeg, 2024. "Benefits of Rent Sharing in Dynamic Resource Games," Dynamic Games and Applications, Springer, vol. 14(1), pages 20-32, March.
    5. Gregor Schwerhoff & Martin Stuermer, 2015. "Non-renewable resources, extraction technology, and endogenous growth," Working Papers 1506, Federal Reserve Bank of Dallas.
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