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Reclamation of a Resource Extraction Site Model with Random Components

Author

Listed:
  • Ekaterina Gromova

    (Transport and Telecommunication Institute, LV-1019 Riga, Latvia)

  • Anastasiia Zaremba

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

  • Nahid Masoudi

    (Department of Economics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada)

Abstract

We compute the cooperative and the Nash equilibrium solutions for the discounted optimal control problem in a two-player differential game of reclamation of a resource extraction site, where each firm’s planning horizon presents the period that extraction of the resources from their site is economically viable. Hence, the planning horizon is defined by a random duration determined on the infinite time horizon. The comparison of the cooperative and Nash solutions and also the comparative statics are provided numerically. We also define the concept of “normalized value of cooperation” and explain how this concept could help us to better characterize the losses the players will face if they continue to refrain from cooperation.

Suggested Citation

  • Ekaterina Gromova & Anastasiia Zaremba & Nahid Masoudi, 2022. "Reclamation of a Resource Extraction Site Model with Random Components," Mathematics, MDPI, vol. 10(24), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4805-:d:1006460
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    References listed on IDEAS

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    1. Simone Marsiglio & Nahid Masoudi, 2022. "Reclamation of a resource extraction site: A differential game approach," Metroeconomica, Wiley Blackwell, vol. 73(3), pages 770-802, July.
    2. Yang, Peifang & Davis, Graham A., 2018. "Non-renewable resource extraction under financial incentives to reduce and reverse stock pollution," Journal of Environmental Economics and Management, Elsevier, vol. 92(C), pages 282-299.
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    4. Steffen Jørgensen & Georges Zaccour, 2007. "Developments in differential game theory and numerical methods: economic and management applications," Computational Management Science, Springer, vol. 4(2), pages 159-181, April.
    5. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, November.
    6. Lappi, Pauli, 2020. "A model of optimal extraction and site reclamation," Resource and Energy Economics, Elsevier, vol. 59(C).
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