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

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  • Roth, Alvin
  • Bereby-Meyer, Yoella

Abstract

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.

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Bibliographic Info

Paper provided by Harvard University Department of Economics in its series Scholarly Articles with number 2580381.

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Date of creation: 2006
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Publication status: Published in American Economic Review
Handle: RePEc:hrv:faseco:2580381

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  1. Stahl, Dale O., 2000. "Rule Learning in Symmetric Normal-Form Games: Theory and Evidence," Games and Economic Behavior, Elsevier, Elsevier, vol. 32(1), pages 105-138, July.
  2. Andreoni, James A & Miller, John H, 1993. "Rational Cooperation in the Finitely Repeated Prisoner's Dilemma: Experimental Evidence," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 103(418), pages 570-85, May.
  3. Sainty, Barbara, 1999. "Achieving greater cooperation in a noisy prisoner's dilemma: an experimental investigation," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 39(4), pages 421-435, July.
  4. Dale O. Stahl, 1999. "Evidence based rules and learning in symmetric normal-form games," International Journal of Game Theory, Springer, Springer, vol. 28(1), pages 111-130.
  5. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, Econometric Society, vol. 47(2), pages 263-91, March.
  6. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Pairwise Kidney Exchange," Game Theory and Information, EconWPA 0408001, EconWPA, revised 16 Feb 2005.
  7. 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, Elsevier, vol. 8(1), pages 164-212.
  8. 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, Elsevier, vol. 39(1), pages 111-128, May.
  9. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, Elsevier, vol. 27(2), pages 245-252, August.
  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, Elsevier, vol. 7(1), pages 47-70, March.
  11. Nick Feltovich & John Duffy, 1999. "Does observation of others affect learning in strategic environments? An experimental study," International Journal of Game Theory, Springer, Springer, vol. 28(1), pages 131-152.
  12. Roth, Alvin & Ünver, M. Utku & Sönmez, Tayfun, 2004. "Kidney Exchange," Scholarly Articles, Harvard University Department of Economics 2580565, Harvard University Department of Economics.
  13. Esther Hauk & Rosemarie Nagel, 2000. "Choice of partners in multiple two-person prisoner's dilemma games: An experimental study," Economics Working Papers, Department of Economics and Business, Universitat Pompeu Fabra 487, Department of Economics and Business, Universitat Pompeu Fabra.
  14. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, Econometric Society, vol. 52(1), pages 87-100, January.
  15. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, Econometric Society, vol. 67(4), pages 827-874, July.
  16. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521536721.
  17. Nick Feltovich, 2000. "Reinforcement-Based vs. Belief-Based Learning Models in Experimental Asymmetric-Information," Econometrica, Econometric Society, Econometric Society, vol. 68(3), pages 605-642, May.
  18. Alvin E. Roth & Tayfun S�nmez, 2005. "A Kidney Exchange Clearinghouse in New England," American Economic Review, American Economic Association, American Economic Association, vol. 95(2), pages 376-380, May.
  19. Cooper, R. & DeJong, D.W. & Ross, T.W., 1992. "Cooperation without Reputation: Experimental Evidence from Prisoner's Dilemma Games," Papers, Boston University - Industry Studies Programme 36, Boston University - Industry Studies Programme.
  20. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive, David K. Levine 624, David K. Levine.
  21. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth & Tayfun S�nmez, 2005. "The Boston Public School Match," American Economic Review, American Economic Association, American Economic Association, vol. 95(2), pages 368-371, May.
  22. Miller, John H., 1996. "The coevolution of automata in the repeated Prisoner's Dilemma," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 29(1), pages 87-112, January.
  23. 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, American Economic Association, vol. 88(4), pages 848-81, September.
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