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Learning, hypothesis testing, and Nash equilibrium

  • Foster, Dean P.
  • Young, H. Peyton

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

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 45 (2003)
Issue (Month): 1 (October)
Pages: 73-96

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Handle: RePEc:eee:gamebe:v:45:y:2003:i:1:p:73-96
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  1. John H. Nachbar, 1997. "Prediction, Optimization, and Learning in Repeated Games," Econometrica, Econometric Society, vol. 65(2), pages 275-310, March.
  2. Dean P Foster, 1997. "A proof of Calibration via Blackwell's Approachability Theorem," Levine's Working Paper Archive 591, David K. Levine.
  3. Ehud Kalai & Ehud Lehrer, 1990. "Rational Learning Leads to Nash Equilibrium," Discussion Papers 895, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Fudenberg, Drew & Levine, David, 1999. "Conditional Universal Consistency," Scholarly Articles 3204826, Harvard University Department of Economics.
  5. Jordan J. S., 1995. "Bayesian Learning in Repeated Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 8-20, April.
  6. Drew Fudenberg & David K. Levine, 1996. "An Easier Way to Calibrate," Levine's Working Paper Archive 2059, David K. Levine.
  7. Sergiu Hart & Andreu Mas-Colell, 1999. "A General Class of Adaptive Strategies," Game Theory and Information 9904001, EconWPA, revised 23 Mar 2000.
  8. S. Hart & A. Mas-Collel, 2010. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Levine's Working Paper Archive 572, David K. Levine.
  9. Nyarko, Yaw, 1994. "Bayesian Learning Leads to Correlated Equilibria in Normal Form Games," Economic Theory, Springer, vol. 4(6), pages 821-41, October.
  10. Jeheil Phillippe, 1995. "Limited Horizon Forecast in Repeated Alternate Games," Journal of Economic Theory, Elsevier, vol. 67(2), pages 497-519, December.
  11. 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.
  12. Dean Foster & Peyton Young, . "Learning with Hazy Beliefs," ELSE working papers 023, ESRC Centre on Economics Learning and Social Evolution.
  13. Ronald Miller & Chris Sanchirico, . "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.
  14. 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.
  15. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July.
  16. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
  17. 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.
  18. Foster, Dean P. & Young, H. Peyton, 1998. "On the Nonconvergence of Fictitious Play in Coordination Games," Games and Economic Behavior, Elsevier, vol. 25(1), pages 79-96, October.
  19. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
  20. John H. Nachbar, 2001. "Bayesian learning in repeated games of incomplete information," Social Choice and Welfare, Springer, vol. 18(2), pages 303-326.
  21. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
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