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Learning Hypothesis Testing and Nash Equilibrium

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Peyton Young

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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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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. Jim Engle-Warnick & Ed Hopkins, 2006. "A Simple Test of Learning Theory?," ESE Discussion Papers 153, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
    Other versions:
  2. Sergiu Hart & Andreu Mas-Colell, 2004. "Stochastic Uncoupled Dynamics and Nash Equilibrium," Economics Working Papers 783, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
    Other versions:
  3. Joseph E. Harrington, Jr. & Joe Chen, 2005. "Cartel Pricing Dynamics with Cost Variability and Endogenous Buyer Detection," CIRJE F-Series CIRJE-F-359, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
    Other versions:
  4. Gordon D. Menzies & Daniel John Zizzo, 2005. "Inferential Expectations," CAMA Working Papers 2005-12, Australian National University, Centre for Applied Macroeconomic Analysis. [Downloadable!]
    Other versions:
  5. H. Peyton Young, 2008. "Learning by Trial and Error," Economics Series Working Papers 384, University of Oxford, Department of Economics. [Downloadable!]
    Other versions:
  6. Fabrizio Germano & Gábor Lugosi, 2004. "Global Nash Convergence of Foster and Young's Regret Testing," Economics Working Papers 788, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
    Other versions:
  7. John H. Nachbar, 2003. "Beliefs in Repeated Games," ISER Discussion Paper 0597, Institute of Social and Economic Research, Osaka University. [Downloadable!]
  8. Timothy N. Cason & Daniel Friedman & Ed Hopkins, 2009. "Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria," ESE Discussion Papers 188, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
  9. Michel Benaim & Josef Hofbauer & Ed Hopkins, 2005. "Learning in Games with Unstable Equilibria," Levine's Bibliography 784828000000000609, UCLA Department of Economics. [Downloadable!]
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  10. H. Peyton Young, 2007. "The Possible and the Impossible in Multi-Agent Learning," Economics Series Working Papers 304, University of Oxford, Department of Economics. [Downloadable!]
  11. Sergiu Hart & Andreu Mas-Colell, 2002. "Uncoupled dynamics cannot lead to Nash equilibrium," Discussion Paper Series dp299, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
  12. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine. [Downloadable!]
  13. Sergiu Hart & Yishay Mansour, 2006. "The Communication Complexity of Uncoupled Nash Equilibrium Procedures," Levine's Bibliography 122247000000001299, UCLA Department of Economics. [Downloadable!]
    Other versions:
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