IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v91y2015icp347-359.html
   My bibliography  Save this article

Polynomial-time computation of exact correlated equilibrium in compact games

Author

Listed:
  • Jiang, Albert Xin
  • Leyton-Brown, Kevin

Abstract

In a landmark paper, Papadimitriou and Roughgarden described a polynomial-time algorithm (“Ellipsoid Against Hope”) for computing sample correlated equilibria of concisely-represented games. Recently, Stein, Parrilo and Ozdaglar showed that this algorithm can fail to find an exact correlated equilibrium. We present a variant of the Ellipsoid Against Hope algorithm that guarantees the polynomial-time identification of exact correlated equilibrium. Our algorithm differs from the original primarily in its use of a separation oracle that produces cuts corresponding to pure-strategy profiles. Our new separation oracle can be understood as a derandomization of Papadimitriou and Roughgarden's original separation oracle via the method of conditional probabilities. We also adapt our techniques to two related algorithms that are based on the Ellipsoid Against Hope approach, Hart and Mansour's communication procedure for correlated equilibria and Huang and von Stengel's algorithm for extensive-form correlated equilibria, in both cases yielding efficient exact solutions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:gamebe:v:91:y:2015:i:c:p:347-359
    DOI: 10.1016/j.geb.2013.02.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825613000249
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2013.02.002?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. Fabrizio Germano & Gábor Lugosi, 2007. "Existence of Sparsely Supported Correlated Equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 575-578, September.
    2. Talman, A.J.J. & van der Laan, G. & Van der Heyden, L., 1987. "Variable dimension algorithms for solving the nonlinear complementarity problem on a product of unit simplices using general labelling," Other publications TiSEM fbe9ae2f-e01d-4eef-944c-6, Tilburg University, School of Economics and Management.
    3. 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.
    4. Myerson, Roger B., 1997. "Dual Reduction and Elementary Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 183-202, October.
    5. Govindan, Srihari & Wilson, Robert, 2003. "A global Newton method to compute Nash equilibria," Journal of Economic Theory, Elsevier, vol. 110(1), pages 65-86, May.
    6. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    7. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    8. 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..
    9. Herbert E. Scarf, 1967. "The Approximation of Fixed Points of a Continuous Mapping," Cowles Foundation Discussion Papers 216R, Cowles Foundation for Research in Economics, Yale University.
    10. Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April.
    11. McKelvey, Richard D. & McLennan, Andrew, 1996. "Computation of equilibria in finite games," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 2, pages 87-142, Elsevier.
    12. 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..
    13. Jiang, Albert Xin & Leyton-Brown, Kevin & Bhat, Navin A.R., 2011. "Action-Graph Games," Games and Economic Behavior, Elsevier, vol. 71(1), pages 141-173, January.
    14. G. van der Laan & A. J. J. Talman & L. van der Heyden, 1987. "Simplicial Variable Dimension Algorithms for Solving the Nonlinear Complementarity Problem on a Product of Unit Simplices Using a General Labelling," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 377-397, August.
    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. Tim Roughgarden, 2018. "Complexity Theory, Game Theory, and Economics: The Barbados Lectures," Papers 1801.00734, arXiv.org, revised Feb 2020.
    2. Hart, Sergiu & Nisan, Noam, 2018. "The query complexity of correlated equilibria," Games and Economic Behavior, Elsevier, vol. 108(C), pages 401-410.
    3. AmirMahdi Ahmadinejad & Sina Dehghani & MohammadTaghi Hajiaghayi & Brendan Lucier & Hamid Mahini & Saeed Seddighin, 2019. "From Duels to Battlefields: Computing Equilibria of Blotto and Other Games," Management Science, INFORMS, vol. 44(4), pages 1304-1325, November.
    4. Babichenko, Yakov & Rubinstein, Aviad, 2022. "Communication complexity of approximate Nash equilibria," Games and Economic Behavior, Elsevier, vol. 134(C), pages 376-398.
    5. Bhaskar, Umang & Ligett, Katrina & Schulman, Leonard J. & Swamy, Chaitanya, 2019. "Achieving target equilibria in network routing games without knowing the latency functions," Games and Economic Behavior, Elsevier, vol. 118(C), pages 533-569.

    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. 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..
    2. Yannick Viossat, 2003. "Geometry, Correlated Equilibria and Zero-Sum Games," Working Papers hal-00242993, HAL.
    3. Cao, Yiyin & Dang, Chuangyin, 2022. "A variant of Harsanyi's tracing procedures to select a perfect equilibrium in normal form games," Games and Economic Behavior, Elsevier, vol. 134(C), pages 127-150.
    4. Tommaso Denti & Doron Ravid, 2023. "Robust Predictions in Games with Rational Inattention," Papers 2306.09964, arXiv.org.
    5. Porter, Ryan & Nudelman, Eugene & Shoham, Yoav, 2008. "Simple search methods for finding a Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 63(2), pages 642-662, July.
    6. Yannick Viossat, 2003. "Properties of Dual Reduction," Working Papers hal-00242992, HAL.
    7. Yannick Viossat, 2010. "Properties and applications of dual reduction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(1), pages 53-68, July.
    8. Thompson, David R.M. & Leyton-Brown, Kevin, 2017. "Computational analysis of perfect-information position auctions," Games and Economic Behavior, Elsevier, vol. 102(C), pages 583-623.
    9. Michael Chwe, 2006. "Statistical Game Theory," Theory workshop papers 815595000000000004, UCLA Department of Economics.
    10. 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.
    11. Yannick Viossat, 2003. "Elementary Games and Games Whose Correlated Equilibrium Polytope Has Full Dimension," Working Papers hal-00242991, HAL.
    12. Viossat, Yannick, 2008. "Is having a unique equilibrium robust?," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1152-1160, December.
    13. Jiang, Albert Xin & Leyton-Brown, Kevin & Bhat, Navin A.R., 2011. "Action-Graph Games," Games and Economic Behavior, Elsevier, vol. 71(1), pages 141-173, January.
    14. 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.
    15. Robert Nau, 2001. "De Finetti was Right: Probability Does Not Exist," Theory and Decision, Springer, vol. 51(2), pages 89-124, December.
    16. Joosten, Reinoud & Talman, Dolf, 1998. "A globally convergent price adjustment process for exchange economies," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 15-26, January.
    17. Fabrizio Germano & Peio Zuazo-Garin, 2017. "Bounded rationality and correlated equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 595-629, August.
    18. 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.
    19. Ozdogan, Ayca & Saglam, Ismail, 2021. "Correlated equilibrium under costly disobedience," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 98-104.
    20. Noah Stein & Asuman Ozdaglar & Pablo Parrilo, 2011. "Structure of extreme correlated equilibria: a zero-sum example and its implications," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 749-767, November.

    More about this item

    Keywords

    Correlated equilibrium; Ellipsoid method; Separation oracle; Derandomization;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    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:eee:gamebe:v:91:y:2015:i:c:p:347-359. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.