IDEAS home Printed from https://ideas.repec.org/a/wsi/igtrxx/v18y2016i02ns0219198916400041.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219198916400041
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219198916400041?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    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.
    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, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    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.

    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. Hassan Benchekroun & Farnaz Taherkhani, 2014. "Adaptation and the Allocation of Pollution Reduction Costs," Dynamic Games and Applications, Springer, vol. 4(1), pages 32-57, March.
    2. Anton Bondarev, 2021. "Games Without Winners: Catching-up with Asymmetric Spillovers," Dynamic Games and Applications, Springer, vol. 11(4), pages 670-703, December.
    3. Ekaterina Marova & Ekaterina Gromova & Polina Barsuk & Anastasia Shagushina, 2020. "On the Effect of the Absorption Coefficient in a Differential Game of Pollution Control," Mathematics, MDPI, vol. 8(6), pages 1-24, June.
    4. Colombo, Luca & Labrecciosa, Paola, 2018. "Consumer surplus-enhancing cooperation in a natural resource oligopoly," Journal of Environmental Economics and Management, Elsevier, vol. 92(C), pages 185-193.
    5. 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.
    6. repec:tiu:tiucen:200880 is not listed on IDEAS
    7. 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.
    8. Açıkgöz, Ömer T. & Benchekroun, Hassan, 2017. "Anticipated international environmental agreements," European Economic Review, Elsevier, vol. 92(C), pages 306-336.
    9. Dmitry Gromov & Ekaterina Gromova, 2017. "On a Class of Hybrid Differential Games," Dynamic Games and Applications, Springer, vol. 7(2), pages 266-288, June.
    10. Guillaume Bataille & Benteng Zou, 2024. "International Fisheries Agreements: Endogenous Exits, Shapley Values, and Moratorium Fishing Policy," AMSE Working Papers 2421, Aix-Marseille School of Economics, France.
    11. Guillaume Bataille & Benteng Zou, 2024. "International Fisheries Agreements: Endogenous Exits, Shapley Values, and Moratorium Fishing Policy," DEM Discussion Paper Series 24-06, Department of Economics at the University of Luxembourg.
    12. Smala Fanokoa, Pascaux & Telahigue, Issam & Zaccour, Georges, 2011. "Buying cooperation in an asymmetric environmental differential game," Journal of Economic Dynamics and Control, Elsevier, vol. 35(6), pages 935-946, June.
    13. Benchekroun, Hassan & Ray Chaudhuri, Amrita, 2011. "Environmental policy and stable collusion: The case of a dynamic polluting oligopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 479-490, April.
    14. N. Baris Vardar & Georges Zaccour, 2020. "Exploitation of a Productive Asset in the Presence of Strategic Behavior and Pollution Externalities," Mathematics, MDPI, vol. 8(10), pages 1-28, October.
    15. G. Zaccour, 2003. "Computation of Characteristic Function Values for Linear-State Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 183-194, April.
    16. Masahiko Hattori & Yasuhito Tanaka, 2019. "General analysis of dynamic oligopoly with sticky price," Economics Bulletin, AccessEcon, vol. 39(4), pages 2990-2998.
    17. Régis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2017. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Working Papers hal-01592958, HAL.
    18. Reinhard Neck & Dmitri Blueschke, 2014. "“Haircuts” for the EMU periphery: virtue or vice?," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 41(2), pages 153-175, May.
    19. A. J. Novak & G. Feichtinger & G. Leitmann, 2010. "A Differential Game Related to Terrorism: Nash and Stackelberg Strategies," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 533-555, March.
    20. Gerhard Sorger, 2005. "A dynamic common property resource problem with amenity value and extraction costs," International Journal of Economic Theory, The International Society for Economic Theory, vol. 1(1), pages 3-19, March.
    21. Denis Claude & Charles Figuières & Mabel Tidball, 2008. "Short-run stick and long-run carrot policy: the role of initial conditions," Working Papers 08-04, LAMETA, Universtiy of Montpellier, revised Feb 2008.

    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:wsi:igtrxx:v:18:y:2016:i:02:n:s0219198916400041. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/igtr/igtr.shtml .

    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.