IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2311.04162.html
   My bibliography  Save this paper

Coarse correlated equilibria in linear quadratic mean field games and application to an emission abatement game

Author

Listed:
  • Luciano Campi
  • Federico Cannerozzi
  • Fanny Cartellier

Abstract

Coarse correlated equilibria (CCE) are a good alternative to Nash equilibria (NE), as they arise more naturally as outcomes of learning algorithms and they may exhibit higher payoffs than NE. CCEs include a device which allows players' strategies to be correlated without any cooperation, only through information sent by a mediator. We develop a methodology to concretely compute mean field CCEs in a linear-quadratic mean field game framework. We compare their performance to mean field control solutions and mean field NE (usually named MFG solutions). Our approach is implemented in the mean field version of an emission abatement game between greenhouse gas emitters. In particular, we exhibit a simple and tractable class of mean field CCEs which allows to outperform very significantly the mean field NE payoff and abatement levels, bridging the gap between the mean field NE and the social optimum obtained by mean field control.

Suggested Citation

  • Luciano Campi & Federico Cannerozzi & Fanny Cartellier, 2023. "Coarse correlated equilibria in linear quadratic mean field games and application to an emission abatement game," Papers 2311.04162, arXiv.org.
    • Handle: RePEc:arx:papers:2311.04162
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2311.04162
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    2. Christine Grüning & Wolfgang Peters, 2010. "Can Justice and Fairness Enlarge International Environmental Agreements?," Games, MDPI, vol. 1(2), pages 1-22, June.
    3. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    4. MOULIN, Hervé & VIAL, Jean-Philippe, 1978. "Strategically zero-sum games: the class of games whose completely mixed equilibria connot be improved upon," LIDAM Reprints CORE 359, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Gilboa, Itzhak & Zemel, Eitan, 1989. "Nash and correlated equilibria: Some complexity considerations," Games and Economic Behavior, Elsevier, vol. 1(1), pages 80-93, March.
    6. Moulin, Herve & Ray, Indrajit & Sen Gupta, Sonali, 2014. "Improving Nash by coarse correlation," Journal of Economic Theory, Elsevier, vol. 150(C), pages 852-865.
    7. Sergiu Hart & Andreu Mas-Colell, 2013. "Regret-Based Continuous-Time Dynamics," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 5, pages 99-124, World Scientific Publishing Co. Pte. Ltd..
    8. repec:cup:cbooks:9781316779309 is not listed on IDEAS
    9. Roughgarden,Tim, 2016. "Twenty Lectures on Algorithmic Game Theory," Cambridge Books, Cambridge University Press, number 9781316624791.
    10. Roughgarden,Tim, 2016. "Twenty Lectures on Algorithmic Game Theory," Cambridge Books, Cambridge University Press, number 9781107172661.
    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. Konstantinos Georgalos & Indrajit Ray & Sonali SenGupta, 2020. "Nash versus coarse correlation," Experimental Economics, Springer;Economic Science Association, vol. 23(4), pages 1178-1204, December.
    2. Awaya, Yu & Krishna, Vijay, 2019. "Communication and cooperation in repeated games," Theoretical Economics, Econometric Society, vol. 14(2), May.
    3. Tommaso Denti & Doron Ravid, 2023. "Robust Predictions in Games with Rational Inattention," Papers 2306.09964, arXiv.org.
    4. Ozdogan, Ayca & Saglam, Ismail, 2021. "Correlated equilibrium under costly disobedience," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 98-104.
    5. Tim Roughgarden, 2018. "Complexity Theory, Game Theory, and Economics: The Barbados Lectures," Papers 1801.00734, arXiv.org, revised Feb 2020.
    6. Grant, Simon & Stauber, Ronald, 2022. "Delegation and ambiguity in correlated equilibrium," Games and Economic Behavior, Elsevier, vol. 132(C), pages 487-509.
    7. Trivikram Dokka Venkata Satyanaraya & Herve Moulin & Indrajit Ray & Sonali Sen Gupta, 2020. "Equilibrium Design by Coarse Correlation in Quadratic Games," Working Papers 301895429, Lancaster University Management School, Economics Department.
    8. Yannick Viossat, 2003. "Geometry, Correlated Equilibria and Zero-Sum Games," Working Papers hal-00242993, HAL.
    9. Bernhard von Stengel & Françoise Forges, 2008. "Extensive-Form Correlated Equilibrium: Definition and Computational Complexity," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 1002-1022, November.
    10. Trivikram Dokka & Hervé Moulin & Indrajit Ray & Sonali SenGupta, 2023. "Equilibrium design in an n-player quadratic game," Review of Economic Design, Springer;Society for Economic Design, vol. 27(2), pages 419-438, June.
    11. Georgalos, Konstantinos & Ray, Indrajit & Gupta, Sonali Sen, 2019. "Nash vs. Coarse Correlation," Cardiff Economics Working Papers E2019/3, Cardiff University, Cardiff Business School, Economics Section.
    12. Friedman, Daniel & Rabanal, Jean Paul & Rud, Olga A. & Zhao, Shuchen, 2022. "On the empirical relevance of correlated equilibrium," Journal of Economic Theory, Elsevier, vol. 205(C).
    13. Moulin, Herve & Ray, Indrajit & Sen Gupta, Sonali, 2014. "Improving Nash by coarse correlation," Journal of Economic Theory, Elsevier, vol. 150(C), pages 852-865.
    14. Ferenc Forgó, 2020. "Exact enforcement value of soft correlated equilibrium for generalized chicken and prisoner’s dilemma games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 209-227, March.
    15. Herve Moulin & Indrajit Ray & Sonali Sen Gupta, 2013. "Coarse Correlated Equilibria in an Abatement Game," Discussion Papers 13-11, Department of Economics, University of Birmingham.
    16. Trivikram Dokka Venkata Satyanaraya & Herve Moulin & Indrajit Ray & Sonali Sen Gupta, 2019. "Improving Abatement Levels and Welfare by Coarse Correlation in an Environmental Game," Working Papers 266042710, Lancaster University Management School, Economics Department.
    17. Hau Chan & Michael Ceyko & Luis Ortiz, 2017. "Interdependent Defense Games with Applications to Internet Security at the Level of Autonomous Systems," Games, MDPI, vol. 8(1), pages 1-60, February.
    18. Stein, Noah D. & Parrilo, Pablo A. & Ozdaglar, Asuman, 2011. "Correlated equilibria in continuous games: Characterization and computation," Games and Economic Behavior, Elsevier, vol. 71(2), pages 436-455, March.
    19. Konstantinos Georgalos & Indrajit Ray & Sonali Sen Gupta, 2017. "Coarse correlation and coordination in a game," Working Papers 151235570, Lancaster University Management School, Economics Department.
    20. Ferenc Forgó, 2011. "Generalized correlated equilibrium for two-person games in extensive form with perfect information," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(2), pages 201-213, June.

    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:2311.04162. 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.