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Improving Nash by Coarse Correlation

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  • Herve Moulin
  • Indrajit Ray
  • Sonali Sen Gupta

Abstract

We consider a class of symmetric two-person quadratic games where coarse correlated equilibria - CCE - (Moulin and Vial 1978) can strictly improve upon the Nash equilibrium payoffs, while correlated equilibrium - CE - (Aumann 1974, 1987) cannot, because these games are potential games. We compute the largest feasible total utility in any CCE in those games, and show that it is achieved by a CCE involving only two pure strategy profiles. Applications include the Cournot duopoly and the game of public good provision, where the improvement over and above the Nash equilibrium payoff can be substantial.

Suggested Citation

  • Herve Moulin & Indrajit Ray & Sonali Sen Gupta, 2013. "Improving Nash by Coarse Correlation," Discussion Papers 13-10, Department of Economics, University of Birmingham.
    • Handle: RePEc:bir:birmec:13-10
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    12. 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.
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    Cited by:

    1. Yu Awaya, 2019. "Collusion and Information Exchange," The Japanese Economic Review, Springer, vol. 70(3), pages 394-402, September.
    2. Ozdogan, Ayca & Saglam, Ismail, 2021. "Correlated equilibrium under costly disobedience," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 98-104.
    3. 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.
    4. 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.
    5. Konstantinos Georgalos & Indrajit Ray & Sonali Sen Gupta, 2017. "Coarse correlation and coordination in a game," Working Papers 151235570, Lancaster University Management School, Economics Department.
    6. 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.
    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. Yu Awaya & Vijay Krishna, 2020. "Information exchange in cartels," RAND Journal of Economics, RAND Corporation, vol. 51(2), pages 421-446, June.
    9. 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.
    10. Awaya, Yu & Krishna, Vijay, 2019. "Communication and cooperation in repeated games," Theoretical Economics, Econometric Society, vol. 14(2), May.
    11. Konstantinos Georgalos & Indrajit Ray & Sonali SenGupta, 2020. "Nash versus coarse correlation," Experimental Economics, Springer;Economic Science Association, vol. 23(4), pages 1178-1204, December.
    12. Grant, Simon & Stauber, Ronald, 2022. "Delegation and ambiguity in correlated equilibrium," Games and Economic Behavior, Elsevier, vol. 132(C), pages 487-509.
    13. Trivikram Dokka & Jorge Bruno & Sonali SenGupta & Chowdhury Mohammad Sakib Anwar, 2022. "Pricing and Electric Vehicle Charging Equilibria," Papers 2210.15035, arXiv.org, revised Dec 2022.
    14. Dokka, Trivikram & Bruno, Jorge & SenGupta, Sonali & Anwar, Sakib, 2022. "Pricing and Electric Vehicle Charging Equilibria," QBS Working Paper Series 2022/10, Queen's University Belfast, Queen's Business School.
    15. 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.
    16. 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.
    17. V. K. Oikonomou & J. Jost, 2013. "Periodic Strategies: A New Solution Concept and an Algorithm for NonTrivial Strategic Form Games," Papers 1307.2035, arXiv.org, revised Jan 2018.
    18. 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.
    19. 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.
    20. Yohan Pelosse, 2024. "Correlated Equilibrium Strategies with Multiple Independent Randomization Devices," Working Papers 2024-05, Swansea University, School of Management.
    21. 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.

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    More about this item

    Keywords

    Coarse correlated equilibrium; Quadratic games; Duopoly models; Public good;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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