IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v153y2012i1d10.1007_s10957-012-9988-6.html
   My bibliography  Save this article

Computation of Correlated Equilibrium with Global-Optimal Expected Social Welfare

Author

Listed:
  • Fook Wai Kong

    (Imperial College)

  • Polyxeni-Margarita Kleniati

    (Imperial College)

  • Berç Rustem

    (Imperial College)

Abstract

In this paper, we propose an algorithm which computes the correlated equilibrium with global-optimal (i.e., maximum) expected social welfare for single stage polynomial games. We first derive tractable primal/dual semidefinite programming (SDP) relaxations for an infinite-dimensional formulation of correlated equilibria. We give an asymptotic convergence proof, which ensures solving the sequence of relaxations leads to solutions that converge to the correlated equilibrium with the highest expected social welfare. Finally, we give a dedicated sequential SDP algorithm and demonstrate it in a wireless application with numerical results.

Suggested Citation

  • Fook Wai Kong & Polyxeni-Margarita Kleniati & Berç Rustem, 2012. "Computation of Correlated Equilibrium with Global-Optimal Expected Social Welfare," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 237-261, April.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:1:d:10.1007_s10957-012-9988-6
    DOI: 10.1007/s10957-012-9988-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-012-9988-6
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-012-9988-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    3. Sergiu Hart & Andreu Mas-Colell, 2013. "A Simple Adaptive Procedure Leading To Correlated Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 2, pages 17-46, World Scientific Publishing Co. Pte. Ltd..
    4. Sergiu Hart & David Schmeidler, 2013. "Existence Of Correlated Equilibria," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 1, pages 3-14, World Scientific Publishing Co. Pte. Ltd..
    5. 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.
    6. Stoltz, Gilles & Lugosi, Gabor, 2007. "Learning correlated equilibria in games with compact sets of strategies," Games and Economic Behavior, Elsevier, vol. 59(1), pages 187-208, April.
    7. Laurent, M., 2009. "Sums of squares, moment matrices and optimization over polynomials," Other publications TiSEM 9fef820b-69d2-43f2-a501-e, Tilburg University, School of Economics and Management.
    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. Fook Kong & Berç Rustem, 2013. "Welfare-maximizing correlated equilibria using Kantorovich polynomials with sparsity," Journal of Global Optimization, Springer, vol. 57(1), pages 251-277, September.

    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. Fook Kong & Berç Rustem, 2013. "Welfare-maximizing correlated equilibria using Kantorovich polynomials with sparsity," Journal of Global Optimization, Springer, vol. 57(1), pages 251-277, September.
    2. Sergiu Hart & Yishay Mansour, 2013. "How Long To Equilibrium? The Communication Complexity Of Uncoupled Equilibrium Procedures," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 10, pages 215-249, World Scientific Publishing Co. Pte. Ltd..
    3. 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.
    4. Rabah Amir & Sergei Belkov & Igor V. Evstigneev, 2017. "Correlated equilibrium in a nutshell," Theory and Decision, Springer, vol. 83(4), pages 457-468, December.
    5. Ozdogan, Ayca & Saglam, Ismail, 2021. "Correlated equilibrium under costly disobedience," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 98-104.
    6. Stoltz, Gilles & Lugosi, Gabor, 2007. "Learning correlated equilibria in games with compact sets of strategies," Games and Economic Behavior, Elsevier, vol. 59(1), pages 187-208, April.
    7. Forges, Françoise & Ray, Indrajit, 2024. "“Subjectivity and correlation in randomized strategies”: Back to the roots," Journal of Mathematical Economics, Elsevier, vol. 114(C).
    8. Ehud Lehrer & Eilon Solan, 2007. "Learning to play partially-specified equilibrium," Levine's Working Paper Archive 122247000000001436, David K. Levine.
    9. Sergiu Hart & Andreu Mas-Colell, 2013. "A Simple Adaptive Procedure Leading To Correlated Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 2, pages 17-46, World Scientific Publishing Co. Pte. Ltd..
    10. Yohan Pelosse, 2024. "Correlated Equilibrium Strategies with Multiple Independent Randomization Devices," Working Papers 2024-05, Swansea University, School of Management.
    11. Hillas, John & Samet, Dov, 2022. "Non-Bayesian correlated equilibrium as an expression of non-Bayesian rationality," Games and Economic Behavior, Elsevier, vol. 135(C), pages 1-15.
    12. Moulin, Herve & Ray, Indrajit & Sen Gupta, Sonali, 2014. "Improving Nash by coarse correlation," Journal of Economic Theory, Elsevier, vol. 150(C), pages 852-865.
    13. Ayala Mashiah-Yaakovi, 2015. "Correlated Equilibria in Stochastic Games with Borel Measurable Payoffs," Dynamic Games and Applications, Springer, vol. 5(1), pages 120-135, March.
    14. Ezra Einy & Ori Haimanko & David Lagziel, 2022. "Strong robustness to incomplete information and the uniqueness of a correlated equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(1), pages 91-119, February.
    15. Soham R. Phade & Venkat Anantharam, 2019. "On the Geometry of Nash and Correlated Equilibria with Cumulative Prospect Theoretic Preferences," Decision Analysis, INFORMS, vol. 16(2), pages 142-156, June.
    16. Jiang, Albert Xin & Leyton-Brown, Kevin, 2015. "Polynomial-time computation of exact correlated equilibrium in compact games," Games and Economic Behavior, Elsevier, vol. 91(C), pages 347-359.
    17. Brendan Kline & Elie Tamer, 2024. "Counterfactual Analysis in Empirical Games," Papers 2410.12731, arXiv.org.
    18. 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.
    19. Kam-Chau Wong & Chongmin Kim, 2004. "Evolutionarily Stable Correlation," Econometric Society 2004 Far Eastern Meetings 495, Econometric Society.
    20. Jann, Ole & Schottmüller, Christoph, 2015. "Correlated equilibria in homogeneous good Bertrand competition," Journal of Mathematical Economics, Elsevier, vol. 57(C), pages 31-37.

    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:spr:joptap:v:153:y:2012:i:1:d:10.1007_s10957-012-9988-6. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.