IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v98y2001i1p26-54.html
   My bibliography  Save this article

A General Class of Adaptive Strategies

Author

Listed:
  • Hart, Sergiu
  • Mas-Colell, Andreu

Abstract

We exhibit and characterize an entire class of simple adaptive strategies, in the repeated play of a game, having the Hannan-consistency property: in the long run, the player is guaranteed an average payoff as large as the best-reply payoff to the empirical distribution of play of the other players; i.e., there is no “regret.” Smooth fictitious play (Fudenberg and Levine 1995) and regret matching (Hart and Mas-Colell 2000) are particular cases. The motivation and application of the current paper come from the study of procedures whose empirical distribution of play is, in the long run, (almost) a correlated equilibrium. For the analysis we first develop a generalization of Blackwell's (1956) approachability strategy for games with vector payoffs.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Hart, Sergiu & Mas-Colell, Andreu, 2001. "A General Class of Adaptive Strategies," Journal of Economic Theory, Elsevier, vol. 98(1), pages 26-54, May.
    • Handle: RePEc:eee:jetheo:v:98:y:2001:i:1:p:26-54
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022-0531(00)92746-7
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    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. D. Blackwell, 2010. "Controlled Random Walks," Levine's Working Paper Archive 465, David K. Levine.
    3. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October.
    4. 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.
    5. D. Foster & R. Vohra, 2010. "Regret in the On-line Decision Problem," Levine's Working Paper Archive 569, David K. Levine.
    6. 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..
    7. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
    8. 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.
    9. D. Blackwell, 2010. "An Analog of the Minmax Theorem for Vector Payoffs," Levine's Working Paper Archive 466, David K. Levine.
    10. D. Foster & R. Vohra, 2010. "Calibrated Learning and Correlated Equilibrium," Levine's Working Paper Archive 568, David K. Levine.
    11. 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.
    12. Monderer, Dov & Samet, Dov & Sela, Aner, 1997. "Belief Affirming in Learning Processes," Journal of Economic Theory, Elsevier, vol. 73(2), pages 438-452, April.
    13. J. Robinson, 1969. "An Iterative Method of Solving a Game," Levine's Working Paper Archive 422, David K. Levine.
    14. N. Littlestone & M. Warmuth, 2010. "The Weighted Majority Algorithm," Levine's Working Paper Archive 575, David K. Levine.
    15. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, April.
    16. Freund, Yoav & Schapire, Robert E., 1999. "Adaptive Game Playing Using Multiplicative Weights," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 79-103, October.
    17. D. Foster & R. Vohra, 2010. "Asymptotic Calibration," Levine's Working Paper Archive 468, David K. Levine.
    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. 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.
    2. Vivaldo M. Mendes & Diana A. Mendes & Orlando Gomes, 2008. "Learning to Play Nash in Deterministic Uncoupled Dynamics," Working Papers Series 1 ercwp1808, ISCTE-IUL, Business Research Unit (BRU-IUL).
    3. Eric Friedman & Scott Shenker & Amy Greenwald, 1998. "Learning in Networks Contexts: Experimental Results from Simulations," Departmental Working Papers 199825, Rutgers University, Department of Economics.
    4. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
    5. Emerson Melo, 2021. "Learning in Random Utility Models Via Online Decision Problems," Papers 2112.10993, arXiv.org, revised Aug 2022.
    6. 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.
    7. Du, Ye & Lehrer, Ehud, 2020. "Constrained no-regret learning," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 16-24.
    8. Nicolò Cesa-Bianchi & Gábor Lugosi & Gilles Stoltz, 2006. "Regret Minimization Under Partial Monitoring," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 562-580, August.
    9. Karl Schlag & Andriy Zapechelnyuk, 2009. "Decision Making in Uncertain and Changing Environments," Discussion Papers 19, Kyiv School of Economics.
    10. Mannor, Shie & Shimkin, Nahum, 2008. "Regret minimization in repeated matrix games with variable stage duration," Games and Economic Behavior, Elsevier, vol. 63(1), pages 227-258, May.
    11. Hofbauer, Josef & Sandholm, William H., 2009. "Stable games and their dynamics," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1665-1693.4, July.
    12. Rene Saran & Roberto Serrano, 2012. "Regret Matching with Finite Memory," Dynamic Games and Applications, Springer, vol. 2(1), pages 160-175, March.
    13. Eric Friedman & Scott Shenker, 1998. "Learning and Implementation on the Internet," Departmental Working Papers 199821, Rutgers University, Department of Economics.
    14. Dean Foster & David K Levine & Rakesh Vohra, 1999. "Introduction to Learning in Games: A Symposium in Honor of David Blackwell," Levine's Working Paper Archive 2091, David K. Levine.
    15. Emerson Melo, 2021. "Learning In Random Utility Models Via Online Decision Problems," CAEPR Working Papers 2022-003 Classification-D, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    16. 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..
    17. Daron Acemoglu & Asuman Ozdaglar, 2011. "Opinion Dynamics and Learning in Social Networks," Dynamic Games and Applications, Springer, vol. 1(1), pages 3-49, March.
    18. Schlag, Karl H. & Zapechelnyuk, Andriy, 2017. "Dynamic benchmark targeting," Journal of Economic Theory, Elsevier, vol. 169(C), pages 145-169.
    19. Burkhard C. Schipper, 2022. "Strategic Teaching and Learning in Games," American Economic Journal: Microeconomics, American Economic Association, vol. 14(3), pages 321-352, August.
    20. Sandroni, Alvaro & Smorodinsky, Rann, 2004. "Belief-based equilibrium," Games and Economic Behavior, Elsevier, vol. 47(1), pages 157-171, April.

    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

    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:jetheo:v:98:y:2001:i:1:p:26-54. 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/622869 .

    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.