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Learning Hypothesis Testing and Nash Equilibrium

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  • 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

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Bibliographic Info

Paper provided by The Johns Hopkins University,Department of Economics in its series Economics Working Paper Archive with number 474.

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Date of creation: Aug 2002
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Handle: RePEc:jhu:papers:474

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  1. Jordan J. S., 1995. "Bayesian Learning in Repeated Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 8-20, April.
  2. John Nachbar, 2010. "Prediction, Optimization and Learning in Repeated Games," Levine's Working Paper Archive 576, David K. Levine.
  3. Sergiu Hart & Andreu Mas-Colell, 1999. "A General Class of Adaptive Strategies," Game Theory and Information 9904001, EconWPA, revised 23 Mar 2000.
  4. Dean P. Foster & H. Peyton Young, 2001. "On the Impossibility of Predicting the Behavior of Rational Agents," Working Papers 01-08-039, Santa Fe Institute.
  5. Nyarko, Yaw, 1994. "Bayesian Learning Leads to Correlated Equilibria in Normal Form Games," Economic Theory, Springer, vol. 4(6), pages 821-41, October.
  6. Fudenberg, Drew & Levine, David, 1999. "An Easier Way to Calibrate," Scholarly Articles 3203773, Harvard University Department of Economics.
  7. Sergiu Hart & Andreu Mas-Colell, 1996. "A simple adaptive procedure leading to correlated equilibrium," Economics Working Papers 200, Department of Economics and Business, Universitat Pompeu Fabra, revised Dec 1996.
  8. 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.
  9. 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.
  10. Dean P. Foster, 1997. "A Proof of Calibration Via Blackwell's Approachability Theorem," Discussion Papers 1182, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Dean Foster & Peyton Young, . "Learning with Hazy Beliefs," ELSE working papers 023, ESRC Centre on Economics Learning and Social Evolution.
  12. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
  13. 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.
  14. Jeheil Phillippe, 1995. "Limited Horizon Forecast in Repeated Alternate Games," Journal of Economic Theory, Elsevier, vol. 67(2), pages 497-519, December.
  15. 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.
  16. 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.
  17. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July.
  18. 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.
  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.
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