IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i24p4805-d1006460.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/24/4805/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/24/4805/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    3. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 32(2), pages 137-150.
    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.
    6. Lappi, Pauli, 2020. "A model of optimal extraction and site reclamation," Resource and Energy Economics, Elsevier, vol. 59(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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. S. Kostyunin & A. Palestini & E. Shevkoplyas, 2014. "On a Nonrenewable Resource Extraction Game Played by Asymmetric Firms," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 660-673, November.
    4. José Daniel López-Barrientos & Ekaterina Viktorovna Gromova & Ekaterina Sergeevna Miroshnichenko, 2020. "Resource Exploitation in a Stochastic Horizon under Two Parametric Interpretations," Mathematics, MDPI, vol. 8(7), pages 1-29, July.
    5. Chan, Chi Kin & Zhou, Yan & Wong, Kar Hung, 2018. "A dynamic equilibrium model of the oligopolistic closed-loop supply chain network under uncertain and time-dependent demands," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 325-354.
    6. Huhtala, Anni & Ropponen, Olli, 2020. "Resource and Environmental Policies for the Mining Industry: What Should Governments Do About the Increasing Social and Environmental Risks?," Working Papers 137, VATT Institute for Economic Research.
    7. Ekaterina Gromova & Anastasiya Malakhova & Arsen Palestini, 2018. "Payoff Distribution in a Multi-Company Extraction Game with Uncertain Duration," Mathematics, MDPI, vol. 6(9), pages 1-17, September.
    8. Eric Innocenti & Corinne Idda & Dominique Prunetti & Pierre-Régis Gonsolin, 2022. "Agent-based modelling of a small-scale fishery in Corsica," Post-Print hal-03886619, HAL.
    9. Aghakazemjourabbaf, Sara & Insley, Margaret, 2021. "Leaving your tailings behind: Environmental bonds, bankruptcy and waste cleanup," Resource and Energy Economics, Elsevier, vol. 65(C).
    10. 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.
    11. Martín-Herrán, Guiomar & Sigué, Simon Pierre & Zaccour, Georges, 2011. "Strategic interactions in traditional franchise systems: Are franchisors always better off?," European Journal of Operational Research, Elsevier, vol. 213(3), pages 526-537, September.
    12. Lappi, Pauli & Lintunen, Jussi, 2021. "From cradle to grave? On optimal nuclear waste disposal," Energy Economics, Elsevier, vol. 103(C).
    13. Mengyuan Zhou, 2022. "Does the Source of Inheritance Matter in Bequest Attitudes? Evidence from Japan," Journal of Family and Economic Issues, Springer, vol. 43(4), pages 867-887, December.
    14. Markku Ollikainen, 1998. "Sustainable Forestry: Timber Bequests, Future Generations and Optimal Tax Policy," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 12(3), pages 255-273, October.
    15. An Chen & Thai Nguyen & Thorsten Sehner, 2022. "Unit-Linked Tontine: Utility-Based Design, Pricing and Performance," Risks, MDPI, vol. 10(4), pages 1-27, April.
    16. Jiang Cheng & Lu Yu, 2019. "Life and health insurance consumption in China: demographic and environmental risks," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 44(1), pages 67-101, January.
    17. Anikó Bíró, 2013. "Subjective mortality hazard shocks and the adjustment of consumption expenditures," Journal of Population Economics, Springer;European Society for Population Economics, vol. 26(4), pages 1379-1408, October.
    18. Masahiko Hattori & Yasuhito Tanaka, 2019. "General analysis of dynamic oligopoly with sticky price," Economics Bulletin, AccessEcon, vol. 39(4), pages 2990-2998.
    19. Frédéric Gannon & Vincent Touzé, 2006. "Insurance and Optimal Growth," Post-Print halshs-00085181, HAL.
    20. Robert Gazzale & Julian Jamison & Alexander Karlan & Dean Karlan, 2013. "Ambiguous Solicitation: Ambiguous Prescription," Economic Inquiry, Western Economic Association International, vol. 51(1), pages 1002-1011, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4805-:d:1006460. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.