IDEAS home Printed from https://ideas.repec.org/p/jhu/papers/474.html
   My bibliography  Save this paper

Learning Hypothesis Testing and Nash Equilibrium

Author

Listed:
  • Peyton Young

Abstract

Although there exist learning processes for which the empirical distribution of play comes close to Nash equilibrium it is an open question whether the players themselves can learn to play equilibrium strategies without assuming that they have prior knowledge of their opponents' strategies and/or payoffs We exhibit a large class of statistical hypotheses testing procedures that solve this problem Consider a finite stage game G that is repeated infinitely often At each time the players have hypotheses about their opponents' repeated game strategies They frequently test their hypotheses against the opponents' recent actions When a hypotheses fails test a new one is adopted Play is almost rational in the sense that at each point of time the players' strategies are є -best replies to their beliefs We show that at least 1 - є of the time t these hypotheses testing strategies constitute an є-equilibrium of the repeated game from t on; in fact the strategies are close to being subgame perfect for long stretches of time Further all players for whom prediction matters ie whose best responses depend on the opponents' behavior learn to predict within є

Suggested Citation

  • Peyton Young, 2002. "Learning Hypothesis Testing and Nash Equilibrium," Economics Working Paper Archive 474, The Johns Hopkins University,Department of Economics.
  • Handle: RePEc:jhu:papers:474
    as

    Download full text from publisher

    File URL: http://econ.jhu.edu/wp-content/uploads/pdf/papers/WP474.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, pages 368-386.
    2. Krishna, Vijay & Rosenthal, Robert W., 1996. "Simultaneous Auctions with Synergies," Games and Economic Behavior, Elsevier, vol. 17(1), pages 1-31, November.
    3. Dean Foster & H Peyton Young, 1999. "On the Impossibility of Predicting the Behavior of Rational Agents," Economics Working Paper Archive 423, The Johns Hopkins University,Department of Economics, revised Jun 2001.
    4. Foster, Dean P., 1999. "A Proof of Calibration via Blackwell's Approachability Theorem," Games and Economic Behavior, Elsevier, pages 73-78.
    5. Foster, Dean P. & Vohra, Rakesh, 1999. "Regret in the On-Line Decision Problem," Games and Economic Behavior, Elsevier, pages 7-35.
    6. Fudenberg, Drew & Levine, David K., 1999. "An Easier Way to Calibrate," Games and Economic Behavior, Elsevier, pages 131-137.
    7. Jerry Green, 2005. "Compensatory transfers in two-player decision problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(2), pages 159-180, June.
    8. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, pages 1019-1045.
    9. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, pages 6-38.
    10. Jordan J. S., 1995. "Bayesian Learning in Repeated Games," Games and Economic Behavior, Elsevier, pages 8-20.
    11. Barton L. Lipman, 2003. "Finite Order Implications of Common Priors," Econometrica, Econometric Society, pages 1255-1267.
    12. Sethi, Rajiv & Somanathan, E., 2001. "Preference Evolution and Reciprocity," Journal of Economic Theory, Elsevier, pages 273-297.
    13. John H. Nachbar, 1997. "Prediction, Optimization, and Learning in Repeated Games," Econometrica, Econometric Society, pages 275-310.
    14. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, pages 104-130.
    15. John H. Nachbar, 2001. "Bayesian learning in repeated games of incomplete information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, pages 303-326.
    16. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, pages 1127-1150.
    17. Foster, Dean P., 1999. "A Proof of Calibration via Blackwell's Approachability Theorem," Games and Economic Behavior, Elsevier, pages 73-78.
    18. Hart, Sergiu & Mas-Colell, Andreu, 2001. "A General Class of Adaptive Strategies," Journal of Economic Theory, Elsevier, pages 26-54.
    19. Ronald Miller & Chris Sanchirico, "undated". "Almost Everybody Disagrees Almost All the Time: The Genericity of Weakly Merging Nowhere," Scholarship at Penn Law upenn_wps-1001, University of Pennsylvania Law School.
    20. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, pages 82-100.
    21. Dean Foster & Peyton Young, "undated". "Learning with Hazy Beliefs," ELSE working papers 023, ESRC Centre on Economics Learning and Social Evolution.
    22. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, pages 40-55.
    23. Sergiu Hart & Andreu Mas-Colell, 1999. "A general class of adaptative strategies," Economics Working Papers 373, Department of Economics and Business, Universitat Pompeu Fabra.
    24. John H. Nachbar, 1997. "Prediction, Optimization, and Learning in Repeated Games," Econometrica, Econometric Society, pages 275-310.
    25. Foster, Dean P. & Young, H. Peyton, 1998. "On the Nonconvergence of Fictitious Play in Coordination Games," Games and Economic Behavior, Elsevier, pages 79-96.
    26. Jeheil Phillippe, 1995. "Limited Horizon Forecast in Repeated Alternate Games," Journal of Economic Theory, Elsevier, pages 497-519.
    27. Nyarko, Yaw, 1994. "Bayesian Learning Leads to Correlated Equilibria in Normal Form Games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 821-841.
    28. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, pages 124-143.
    Full references (including those not matched with items on IDEAS)

    More about this item

    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:jhu:papers:474. 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: (None). General contact details of provider: http://edirc.repec.org/data/dejhuus.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 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 profile, as there may be some citations waiting for confirmation.

    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.