IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2404.15079.html
   My bibliography  Save this paper

Cooperation, Correlation and Competition in Ergodic $N$-player Games and Mean-field Games of Singular Controls: A Case Study

Author

Listed:
  • Federico Cannerozzi
  • Giorgio Ferrari

Abstract

We consider ergodic symmetric $N$-player and mean-field games of singular control in both cooperative and competitive settings. The state process dynamics of a representative player follow geometric Brownian motion, controlled additively through a nondecreasing process. Agents aim to maximize a long-time average reward functional with instantaneous profit of power type. The game shows strategic complementarities, in that the marginal profit function is increasing with respect to the dynamic average of the states of the other players, when $N

Suggested Citation

  • Federico Cannerozzi & Giorgio Ferrari, 2024. "Cooperation, Correlation and Competition in Ergodic $N$-player Games and Mean-field Games of Singular Controls: A Case Study," Papers 2404.15079, arXiv.org.
    • Handle: RePEc:arx:papers:2404.15079
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2404.15079
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rene Carmona & Francois Delarue & Daniel Lacker, 2016. "Mean field games of timing and models for bank runs," Papers 1606.03709, arXiv.org, revised Jan 2017.
    2. Dianetti, Jodi & Ferrari, Giorgio & Tzouanas, Ioannis, 2023. "Ergodic Mean-Field Games of Singular Control with Regime-Switching (extended version)," Center for Mathematical Economics Working Papers 681, Center for Mathematical Economics, Bielefeld University.
    3. Fu, Guanxing & Horst, Ulrich, 2017. "Mean Field Games with Singular Controls," Rationality and Competition Discussion Paper Series 22, CRC TRR 190 Rationality and Competition.
    4. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    5. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    6. Fernando Alvarez & Francesco Lippi & Panagiotis Souganidis, 2023. "Price Setting With Strategic Complementarities as a Mean Field Game," Econometrica, Econometric Society, vol. 91(6), pages 2005-2039, November.
    7. 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).
    8. Moulin, Herve & Ray, Indrajit & Sen Gupta, Sonali, 2014. "Improving Nash by coarse correlation," Journal of Economic Theory, Elsevier, vol. 150(C), pages 852-865.
    9. Luis H. R. Alvarez, 2001. "Reward functionals, salvage values, and optimal stopping," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(2), pages 315-337, December.
    10. Soren Christensen & Berenice Anne Neumann & Tobias Sohr, 2020. "Competition versus Cooperation: A class of solvable mean field impulse control problems," Papers 2010.06452, arXiv.org, revised Apr 2021.
    11. Fernando E. Alvarez & David Argente & Francesco Lippi & Esteban Méndez & Diana Van Patten, 2023. "Strategic Complementarities in a Dynamic Model of Technology Adoption: P2P Digital Payments," NBER Working Papers 31280, National Bureau of Economic Research, Inc.
    12. Vives, Xavier, 2005. "Games with strategic complementarities: New applications to industrial organization," International Journal of Industrial Organization, Elsevier, vol. 23(7-8), pages 625-637, September.
    13. Sachin Adlakha & Ramesh Johari, 2013. "Mean Field Equilibrium in Dynamic Games with Strategic Complementarities," Operations Research, INFORMS, vol. 61(4), pages 971-989, August.
    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. Cannerozzi, Federico & Ferrari, Giorgio, 2024. "Cooperation, Correlation and Competition in Ergodic $N$-Player Games and Mean-Field Games of Singular Controls: A Case Study," Center for Mathematical Economics Working Papers 691, Center for Mathematical Economics, Bielefeld University.
    2. Konstantinos Georgalos & Indrajit Ray & Sonali SenGupta, 2020. "Nash versus coarse correlation," Experimental Economics, Springer;Economic Science Association, vol. 23(4), pages 1178-1204, December.
    3. Ozdogan, Ayca & Saglam, Ismail, 2021. "Correlated equilibrium under costly disobedience," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 98-104.
    4. Yohan Pelosse, 2024. "Correlated Equilibrium Strategies with Multiple Independent Randomization Devices," Working Papers 2024-05, Swansea University, School of Management.
    5. Dianetti, Jodi & Ferrari, Giorgio & Fischer, Markus & Nendel, Max, 2019. "Submodular Mean Field Games. Existence and Approximation of Solutions," Center for Mathematical Economics Working Papers 621, Center for Mathematical Economics, Bielefeld University.
    6. Grant, Simon & Stauber, Ronald, 2022. "Delegation and ambiguity in correlated equilibrium," Games and Economic Behavior, Elsevier, vol. 132(C), pages 487-509.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    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. Dianetti, Jodi & Ferrari, Giorgio & Fischer, Markus & Nendel, Max, 2022. "A Unifying Framework for Submodular Mean Field Games," Center for Mathematical Economics Working Papers 661, Center for Mathematical Economics, Bielefeld University.
    13. Anna Kerkhof & Johannes Münster, 2023. "Strategic Complementarities in a Model of Commercial Media Bias," ECONtribute Discussion Papers Series 261, University of Bonn and University of Cologne, Germany.
    14. 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).
    15. Stefanos Leonardos & Costis Melolidakis, 2018. "On the Commitment Value and Commitment Optimal Strategies in Bimatrix Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-28, September.
    16. Giuseppe Attanasi & Kene Boun My & Nikolaos Georgantzís & Miguel Ginés, 2019. "Strategic Ethics: Altruism without the Other-Regarding Confound," Revue économique, Presses de Sciences-Po, vol. 70(6), pages 967-998.
    17. Anbarcı, Nejat & Feltovich, Nick & Gürdal, Mehmet Y., 2018. "Payoff inequity reduces the effectiveness of correlated-equilibrium recommendations," European Economic Review, Elsevier, vol. 108(C), pages 172-190.
    18. Haoyang Cao & Jodi Dianetti & Giorgio Ferrari, 2021. "Stationary Discounted and Ergodic Mean Field Games of Singular Control," Papers 2105.07213, arXiv.org.
    19. Anna Kerkhof & Johannes Münster, 2023. "Strategic Complementarities in a Model of Commercial Media Bias," CESifo Working Paper Series 10738, CESifo.
    20. Dianetti, Jodi & Ferrari, Giorgio, 2019. "Nonzero-Sum Submodular Monotone-Follower Games. Existence and Approximation of Nash Equilibria," Center for Mathematical Economics Working Papers 605, Center for Mathematical Economics, Bielefeld University.

    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:2404.15079. 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.