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A Differential Game Model for The Extraction of Nonrenewable Resources with Random Initial Times — The Cooperative and Competitive Cases

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  • Ekaterina Viktorovna Gromova

    (Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, Universitetskii Prospekt 35, Petergof, Saint Petersburg, 198504, Russia)

  • José Daniel López-Barrientos

    (Facultad de Ciencias Actuariales, Universidad Anáhuac México Norte Av. Universidad Anáhuac, 46, Col. Lomas Anáhuac Huixquilucan, Edo. de México, México C. P. 52786)

Abstract

In this work, we propose a model for the extraction of a nonrenewable resource in an economy where, initially, only one agent is enabled to perform extraction tasks. However, at certain nonpredictable (random) times, more companies receive the government’s approval for extracting the country’s resources. We provide a setup suitable for the use of standard dynamic programming results for both, the competitive and cooperative schemes; we develop the corresponding HJB equations, prove a verification theorem, and give an example. Our framework is inspired by the trends that oil industries are experiencing in countries like Mexico and Russia.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:igtrxx:v:18:y:2016:i:02:n:s0219198916400041
    DOI: 10.1142/S0219198916400041
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    References listed on IDEAS

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    1. 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.
    2. Pierre Cardaliaguet & Slawomir Plaskacz, 2003. "Existence and uniqueness of a Nash equilibrium feedback for a simple nonzero-sum differential game," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 33-71, December.
    3. Nikolaos Chr. Kakogiannis, 2013. "Decision Making in Energy Market with Producers with Different Profiles," SPOUDAI Journal of Economics and Business, SPOUDAI Journal of Economics and Business, University of Piraeus, vol. 63(1-2), pages 75-93, June.
    4. 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.
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    Cited by:

    1. Rigoberto Real-Miranda & José Daniel López-Barrientos, 2022. "A Geologic-Actuarial Approach for Insuring the Extraction Tasks of Non-Renewable Resources by One and Two Agents," Mathematics, MDPI, vol. 10(13), pages 1-19, June.
    2. Mario A. García-Meza & Ekaterina Viktorovna Gromova & José Daniel López-Barrientos, 2018. "Stable Marketing Cooperation in a Differential Game for an Oligopoly," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-18, September.
    3. Alessandra Buratto & Stefan Wrzaczek, 2018. "Advertising a product to face a competitor entry: a differential game approach," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 463-487, 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.

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