IDEAS home Printed from https://ideas.repec.org/a/ecm/emetrp/v68y2000i5p1127-1150.html
   My bibliography  Save this article

A Simple Adaptive Procedure Leading to Correlated Equilibrium

Author

Listed:
  • Sergiu Hart
  • Andreu Mas-Colell

Abstract

We propose a new and simple adaptive procedure for playing a game: “regret-matching.” In this procedure, players may depart from their current play with probabilities that are proportional to measures of regret for not having used other strategies in the past. It is shown that our adaptive procedure guarantees that, with probability one, the empirical distributions of play converge to the set of correlated equilibria of the game.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
  • Handle: RePEc:ecm:emetrp:v:68:y:2000:i:5:p:1127-1150
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. Sanchirico, Chris William, 1996. "A Probabilistic Model of Learning in Games," Econometrica, Econometric Society, vol. 64(6), pages 1375-1393, November.
    3. Foster, Dean P. & Vohra, Rakesh, 1999. "Regret in the On-Line Decision Problem," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 7-35, October.
    4. Fudenberg, Drew & Levine, David K., 1995. "Consistency and cautious fictitious play," Journal of Economic Dynamics and Control, Elsevier, vol. 19(5-7), pages 1065-1089.
    5. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    6. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    7. Sergiu Hart & Andreu Mas-Colell, 2013. "A General Class Of Adaptive Strategies," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 3, pages 47-76, World Scientific Publishing Co. Pte. Ltd..
    8. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
    9. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
    10. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
    11. Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206, April.
      • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636, April.
    12. Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April.
    13. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-881, September.
    14. Myerson, Roger B., 1997. "Dual Reduction and Elementary Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 183-202, October.
    15. 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..
    16. Nimrod Megiddo, 1979. "On Repeated Games with Incomplete Information Played by Non-Bayesian Players," Discussion Papers 373, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    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. Schlag, Karl H. & Zapechelnyuk, Andriy, 2017. "Dynamic benchmark targeting," Journal of Economic Theory, Elsevier, vol. 169(C), pages 145-169.
    2. Eric Friedman & Scott Shenker & Amy Greenwald, 1998. "Learning in Networks Contexts: Experimental Results from Simulations," Departmental Working Papers 199825, Rutgers University, Department of Economics.
    3. Yannick Viossat, 2003. "Geometry, Correlated Equilibria and Zero-Sum Games," Working Papers hal-00242993, HAL.
    4. Ehud Lehrer & Eilon Solan, 2007. "Learning to play partially-specified equilibrium," Levine's Working Paper Archive 122247000000001436, David K. Levine.
    5. Karl Schlag & Andriy Zapechelnyuk, 2009. "Decision Making in Uncertain and Changing Environments," Discussion Papers 19, Kyiv School of Economics.
    6. Yannick Viossat, 2003. "Properties of Dual Reduction," Working Papers hal-00242992, HAL.
    7. Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2006. "Stochastic Approximations and Differential Inclusions, Part II: Applications," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 673-695, November.
    8. Chernov, G. & Susin, I., 2019. "Models of learning in games: An overview," Journal of the New Economic Association, New Economic Association, vol. 44(4), pages 77-125.
    9. Germano, Fabrizio & Lugosi, Gabor, 2007. "Global Nash convergence of Foster and Young's regret testing," Games and Economic Behavior, Elsevier, vol. 60(1), pages 135-154, July.
    10. Sergiu Hart & Andreu Mas-Colell, 2013. "A General Class Of Adaptive Strategies," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 3, pages 47-76, World Scientific Publishing Co. Pte. Ltd..
    11. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.
    12. Eric Friedman & Scott Shenker, 1998. "Learning and Implementation on the Internet," Departmental Working Papers 199821, Rutgers University, Department of Economics.
    13. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
    14. Ianni, A., 2002. "Reinforcement learning and the power law of practice: some analytical results," Discussion Paper Series In Economics And Econometrics 203, Economics Division, School of Social Sciences, University of Southampton.
    15. 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.
    16. Ho, Teck H. & Camerer, Colin F. & Chong, Juin-Kuan, 2007. "Self-tuning experience weighted attraction learning in games," Journal of Economic Theory, Elsevier, vol. 133(1), pages 177-198, March.
    17. James Andreoni & Marco Castillo & Ragan Petrie, 2009. "Revealing Preferences for Fairness in Ultimatum Bargaining," Korean Economic Review, Korean Economic Association, vol. 25, pages 35-63.
    18. Lehrer, Ehud, 2003. "A wide range no-regret theorem," Games and Economic Behavior, Elsevier, vol. 42(1), pages 101-115, January.
    19. Yannick Viossat, 2003. "Elementary Games and Games Whose Correlated Equilibrium Polytope Has Full Dimension," Working Papers hal-00242991, HAL.
    20. 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.

    More about this item

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary 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:ecm:emetrp:v:68:y:2000:i:5:p:1127-1150. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/essssea.html .

    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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.