IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1710.05131.html
   My bibliography  Save this paper

Mean Field Game Approach to Production and Exploration of Exhaustible Commodities

Author

Listed:
  • Michael Ludkovski
  • Xuwei Yang

Abstract

In a game theoretic framework, we study energy markets with a continuum of homogenous producers who produce energy from an exhaustible resource such as oil. Each producer simultaneously optimizes production rate that drives her revenues, as well as exploration effort to replenish her reserves. This exploration activity is modeled through a controlled point process that leads to stochastic increments to reserves level. The producers interact with each other through the market price that depends on the aggregate production. We employ a mean field game approach to solve for a Markov Nash equilibrium and develop numerical schemes to solve the resulting system of non-local HJB and transport equations with non-local coupling. A time-stationary formulation is also explored, as well as the fluid limit where exploration becomes deterministic.

Suggested Citation

  • Michael Ludkovski & Xuwei Yang, 2017. "Mean Field Game Approach to Production and Exploration of Exhaustible Commodities," Papers 1710.05131, arXiv.org.
    • Handle: RePEc:arx:papers:1710.05131
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1710.05131
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Olivier Guéant & Pierre Louis Lions & Jean-Michel Lasry, 2011. "Mean Field Games and Applications," Post-Print hal-01393103, HAL.
    2. Arrow, Kenneth J. & Chang, Sheldon, 1982. "Optimal pricing, use, and exploration of uncertain natural resource stocks," Journal of Environmental Economics and Management, Elsevier, vol. 9(1), pages 1-10, March.
    3. Deshmukh, Sudhakar D & Pliska, Stanley R, 1980. "Optimal Consumption and Exploration of Nonrenewable Resources under Uncertainty," Econometrica, Econometric Society, vol. 48(1), pages 177-200, January.
    4. Pindyck, Robert S, 1978. "The Optimal Exploration and Production of Nonrenewable Resources," Journal of Political Economy, University of Chicago Press, vol. 86(5), pages 841-861, October.
    5. Patrick Hagan & Diana Woodward & Russel Caflisch & Joseph Keller, 1994. "Optimal pricing, use and exploration of uncertain natural resources," Applied Mathematical Finance, Taylor & Francis Journals, vol. 1(1), pages 87-108.
    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. Ryan Donnelly & Tim Leung, 2019. "Effort Expenditure For Cash Flow In A Mean-Field Equilibrium," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-23, June.
    2. Vicknair, David & Tansey, Michael & O'Brien, Thomas E., 2022. "Measuring fossil fuel reserves: A simulation and review of the U.S. Securities and Exchange Commission approach," Resources Policy, Elsevier, vol. 79(C).
    3. Steven Campbell & Yichao Chen & Arvind Shrivats & Sebastian Jaimungal, 2021. "Deep Learning for Principal-Agent Mean Field Games," Papers 2110.01127, arXiv.org.
    4. Ryan Donnelly & Zi Li, 2022. "Dynamic Inventory Management with Mean-Field Competition," Papers 2210.17208, arXiv.org.
    5. Arvind V. Shrivats & Dena Firoozi & Sebastian Jaimungal, 2022. "A mean‐field game approach to equilibrium pricing in solar renewable energy certificate markets," Mathematical Finance, Wiley Blackwell, vol. 32(3), pages 779-824, July.
    6. Dena Firoozi & Arvind V Shrivats & Sebastian Jaimungal, 2021. "Principal agent mean field games in REC markets," Papers 2112.11963, arXiv.org, revised Jun 2022.

    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. Güntner, Jochen H.F., 2019. "How do oil producers respond to giant oil field discoveries?," Energy Economics, Elsevier, vol. 80(C), pages 59-74.
    2. Gérard Gaudet, 2007. "Natural resource economics under the rule of Hotelling," Canadian Journal of Economics, Canadian Economics Association, vol. 40(4), pages 1033-1059, November.
    3. Tsur, Yacov, 1992. "Stock Uncertainty In Renewable Resource Theory: The Exploitation Of Aquifers Of Unknown Size," Staff Papers 14208, University of Minnesota, Department of Applied Economics.
    4. Rahman, Shaikh Mahfuzur & Helal, Uddin, 2004. "Optimal Contracts For Exploration With Cost Recovery Of An Exhaustible Natural Resource Under Asymmetric Information," 2004 Annual meeting, August 1-4, Denver, CO 20180, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    5. Mohr, Ernst, 1985. "Appropriation of common access natural resources through exploration: A differential game of a claiming rush," Discussion Papers, Series I 206, University of Konstanz, Department of Economics.
    6. Jakobsson, Kristofer & Söderbergh, Bengt & Snowden, Simon & Li, Chuan-Zhong & Aleklett, Kjell, 2012. "Oil exploration and perceptions of scarcity: The fallacy of early success," Energy Economics, Elsevier, vol. 34(4), pages 1226-1233.
    7. Zongxi Li & A. Max Reppen & Ronnie Sircar, 2019. "A Mean Field Games Model for Cryptocurrency Mining," Papers 1912.01952, arXiv.org, revised Jan 2022.
    8. Jeffrey A. Krautkraemer, 1998. "Nonrenewable Resource Scarcity," Journal of Economic Literature, American Economic Association, vol. 36(4), pages 2065-2107, December.
    9. Helal, Uddin & Rahman, Shaikh Mahfuzur, 2006. "Optimal Contracts for Exploration with Cost Recovery of an Exhaustible Natural Resource Under Asymmetric Information," Working Papers 28578, University of Maryland, Department of Agricultural and Resource Economics.
    10. Luca Lambertini, 2014. "Exploration For Nonrenewable Resources In A Dynamic Oligopoly: An Arrovian Result," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 1-11.
    11. Julien Daubanes & Pierre Lasserre, 2019. "The supply of non-renewable resources," Canadian Journal of Economics, Canadian Economics Association, vol. 52(3), pages 1084-1111, August.
    12. Sudhakar D. Deshmukh & Stanley R. Pliska, 1981. "Optimal Consumption of A Nonrenewable Resource with Stochastic Discoveries and a Random Environment," Discussion Papers 500, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    13. Boyce, John R. & Vojtassak, Lucia, 2008. "An 'oil'igopoly theory of exploration," Resource and Energy Economics, Elsevier, vol. 30(3), pages 428-454, August.
    14. Reynolds, Douglas B. & Baek, Jungho, 2012. "Much ado about Hotelling: Beware the ides of Hubbert," Energy Economics, Elsevier, vol. 34(1), pages 162-170.
    15. Eiji Sawada & Shunsuke Managi, 2013. "Non-renewable Resource Extraction with Extraction and Exploration Technologies," Keio/Kyoto Joint Global COE Discussion Paper Series 2012-048, Keio/Kyoto Joint Global COE Program.
    16. van der Ploeg, Frederick & Rezai, Armon, 2020. "The risk of policy tipping and stranded carbon assets," Journal of Environmental Economics and Management, Elsevier, vol. 100(C).
    17. Nyambuu, Unurjargal & Semmler, Willi, 2014. "Trends in the extraction of non-renewable resources: The case of fossil energy," Economic Modelling, Elsevier, vol. 37(C), pages 271-279.
    18. Okullo, Samuel J. & Reynès, Frédéric & Hofkes, Marjan W., 2015. "Modeling peak oil and the geological constraints on oil production," Resource and Energy Economics, Elsevier, vol. 40(C), pages 36-56.
    19. Rick Van der Ploeg & Armon Rezai, 2018. "Climate Policy and Stranded Carbon Assets: A Financial Perspective," OxCarre Working Papers 206, Oxford Centre for the Analysis of Resource Rich Economies, University of Oxford.
    20. Elin Berg & Snorre Kverndokk & Knut Einar Rosendahl, 1999. "Optimal Oil Exploration under Climate Treaties," Discussion Papers 245, Statistics Norway, Research Department.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:1710.05131. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.