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Mean Field Games and Oil Production

Author

Listed:
  • Olivier Guéant

    (LJLL - Laboratoire Jacques-Louis Lions - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Michel Lasry

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Pierre Louis Lions

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, Collège de France - Chaire Équations aux dérivées partielles et applications - CdF (institution) - Collège de France)

Abstract

In this paper we study the evolution of oil production in the long run. A first optimization model is presented, that can be solved using Euler-Lagrange tools. Because these classical tools are not the best suited to the model, we adopt a mean field games approach based on two partial differential equations. An extended model is then presented to analyze the influence of new competitors which might enter the market with energy from renewable sources. The usefulness of a subsidy to potential entrants is discussed.

Suggested Citation

  • Olivier Guéant & Jean-Michel Lasry & Pierre Louis Lions, 2010. "Mean Field Games and Oil Production," Post-Print hal-01393104, HAL.
    • Handle: RePEc:hal:journl:hal-01393104
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    Citations

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    Cited by:

    1. Masaaki Fujii & Akihiko Takahashi, 2021. "Equilibrium Price Formation with a Major Player and its Mean Field Limit," CARF F-Series CARF-F-509, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Masaaki Fujii & Akihiko Takahashi, 2021. "A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition," CARF F-Series CARF-F-521, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Masaaki Fujii & Akihiko Takahashi, 2021. "A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition," CIRJE F-Series CIRJE-F-1177, CIRJE, Faculty of Economics, University of Tokyo.
    4. Masaaki Fujii & Akihiko Takahashi, 2020. "A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition," CIRJE F-Series CIRJE-F-1144, CIRJE, Faculty of Economics, University of Tokyo.
    5. Bouveret, Géraldine & Dumitrescu, Roxana & Tankov, Peter, 2022. "Technological change in water use: A mean-field game approach to optimal investment timing," Operations Research Perspectives, Elsevier, vol. 9(C).
    6. Masaaki Fujii & Akihiko Takahashi, 2020. "A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition," Papers 2003.03035, arXiv.org, revised Sep 2021.
    7. Masaaki Fujii & Akihiko Takahashi, 2020. "A Finite Agent Equilibrium in an Incomplete Market and its Strong Convergence to the Mean-Field Limit," CARF F-Series CARF-F-495, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    8. Masaaki Fujii & Akihiko Takahashi, 2021. "``Equilibrium Price Formation with a Major Player and its Mean Field Limit''," CIRJE F-Series CIRJE-F-1162, CIRJE, Faculty of Economics, University of Tokyo.
    9. Masaaki Fujii & Akihiko Takahashi, 2020. "A Finite Agent Equilibrium in an Incomplete Market and its Strong Convergence to the Mean-Field Limit," CIRJE F-Series CIRJE-F-1156, CIRJE, Faculty of Economics, University of Tokyo.
    10. Masaaki Fujii, 2020. "Probabilistic Approach to Mean Field Games and Mean Field Type Control Problems with Multiple Populations," CARF F-Series CARF-F-497, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    11. Masaaki Fujii & Akihiko Takahashi, 2021. "Equilibrium Price Formation with a Major Player and its Mean Field Limit," Papers 2102.10756, arXiv.org, revised Feb 2022.
    12. Masaaki Fujii & Akihiko Takahashi, 2020. "A Mean Field Game Approach to Equilibrium Pricing with Market Clearing Condition," CARF F-Series CARF-F-473, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    13. Masaaki Fujii & Akihiko Takahashi, 2020. "Strong Convergence to the Mean-Field Limit of A Finite Agent Equilibrium," Papers 2010.09186, arXiv.org, revised Dec 2021.

    More about this item

    Keywords

    Mean field games;

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