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The Speed of Learning in Noisy Games: Partial Reinforcement and the Sustainability of Cooperation

  • Yoella Bereby-Meyer
  • Alvin E. Roth

In an experiment, players? ability to learn to cooperate in the repeated prisoner?s dilemma was substantially diminished when the payoffs were noisy, even though players could monitor one another?s past actions perfectly. In contrast, in one-time play against a succession of opponents, noisy payoffs increased cooperation, by slowing the rate at which cooperation decays. These observations are consistent with the robust observation from the psychology literature that partial reinforcement (adding randomness to the link between an action and its consequences while holding expected payoffs constant) slows learning. This effect is magnified in the repeated game: when others are slow to learn to cooperate, the benefits of cooperation are reduced, which further hampers cooperation. These results show that a small change in the payoff environment, which changes the speed of individual learning, can have a large effect on collective behavior. And they show that there may be interesting comparative dynamics that can be derived from careful attention to the fact that at least some economic behavior is learned from experience. (JEL C71, C72, C73, D83)

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Article provided by American Economic Association in its journal American Economic Review.

Volume (Year): 96 (2006)
Issue (Month): 4 (September)
Pages: 1029-1042

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Handle: RePEc:aea:aecrev:v:96:y:2006:i:4:p:1029-1042
Note: DOI: 10.1257/aer.96.4.1029
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  1. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
  2. Edward J Green & Robert H Porter, 1997. "Noncooperative Collusion Under Imperfect Price Information," Levine's Working Paper Archive 1147, David K. Levine.
  3. Andreoni, J. & Miller, J.H., 1991. "Rational Cooperative in the Finitely Repeated Prisoner's Dilemma: Experimental Evidence," Working papers 9102, Wisconsin Madison - Social Systems.
  4. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth & Tayfun S�nmez, 2005. "The Boston Public School Match," American Economic Review, American Economic Association, vol. 95(2), pages 368-371, May.
  5. Dale O. Stahl, 1997. "Rule Learning in Symmetric Normal-Form Games: Theory and Evidence," CARE Working Papers 9710, The University of Texas at Austin, Center for Applied Research in Economics.
  6. David Kreps & Paul Milgrom & John Roberts & Bob Wilson, 2010. "Rational Cooperation in the Finitely Repeated Prisoners' Dilemma," Levine's Working Paper Archive 239, David K. Levine.
  7. repec:cup:cbooks:9780521551847 is not listed on IDEAS
  8. Alvin E. Roth & Tayfun Sonmez & M. Utku Unver, 2004. "Pairwise Kidney Exchange," NBER Working Papers 10698, National Bureau of Economic Research, Inc.
  9. Alvin E. Roth & Tayfun Sonmez & M. Utku Unver, 2003. "Kidney Exchange," NBER Working Papers 10002, National Bureau of Economic Research, Inc.
  10. Selten, Reinhard & Stoecker, Rolf, 1986. "End behavior in sequences of finite Prisoner's Dilemma supergames A learning theory approach," Journal of Economic Behavior & Organization, Elsevier, vol. 7(1), pages 47-70, March.
  11. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth, 2005. "The New York City High School Match," American Economic Review, American Economic Association, vol. 95(2), pages 364-367, May.
  12. Russell Cooper & Douglas V. DeJong & Thomas W. Ross, 1992. "Cooperation without Reputation: Experimental Evidence from Prisoner's Dilemma Games," Papers 0036, Boston University - Industry Studies Programme.
  13. Erev, Ido & Bereby-Meyer, Yoella & Roth, Alvin E., 1999. "The effect of adding a constant to all payoffs: experimental investigation, and implications for reinforcement learning models," Journal of Economic Behavior & Organization, Elsevier, vol. 39(1), pages 111-128, May.
  14. Miller, John H., 1996. "The coevolution of automata in the repeated Prisoner's Dilemma," Journal of Economic Behavior & Organization, Elsevier, vol. 29(1), pages 87-112, January.
  15. Dale O. Stahl, 1999. "Evidence based rules and learning in symmetric normal-form games," International Journal of Game Theory, Springer, vol. 28(1), pages 111-130.
  16. repec:cup:cbooks:9780521536721 is not listed on IDEAS
  17. Roth, Alvin & Ünver, M. Utku & Sönmez, Tayfun, 2005. "A Kidney Exchange Clearinghouse in New England," Scholarly Articles 2562810, Harvard University Department of Economics.
  18. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  19. John Duffy & Nick Feltovich, 1997. "Does Observation of Others Affect Learning in Strategic Environments? An Experimental Study," Levine's Working Paper Archive 592, David K. Levine.
  20. Jonathan Bendor, 1993. "Uncertainty and the Evolution of Cooperation," Journal of Conflict Resolution, Peace Science Society (International), vol. 37(4), pages 709-734, December.
  21. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
  22. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
  23. Esther Hauk & Rosemarie Nagel, 2000. "Choice of partners in multiple two-person prisoner's dilemma games: An experimental study," Economics Working Papers 487, Department of Economics and Business, Universitat Pompeu Fabra.
  24. Nick Feltovich, 2000. "Reinforcement-Based vs. Belief-Based Learning Models in Experimental Asymmetric-Information," Econometrica, Econometric Society, vol. 68(3), pages 605-642, May.
  25. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-81, September.
  26. Sainty, Barbara, 1999. "Achieving greater cooperation in a noisy prisoner's dilemma: an experimental investigation," Journal of Economic Behavior & Organization, Elsevier, vol. 39(4), pages 421-435, July.
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