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

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Yoella Bereby-Meyer
Alvin E. Roth

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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. (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

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Pairwise Kidney Exchange," Game Theory and Information 0408001, EconWPA, revised 16 Feb 2005. [Downloadable!]
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  2. 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. [Downloadable!] (restricted)
  3. Stahl, Dale O., 2000. "Rule Learning in Symmetric Normal-Form Games: Theory and Evidence," Games and Economic Behavior, Elsevier, vol. 32(1), pages 105-138, July. [Downloadable!] (restricted)
  4. Alvin E. Roth & Tayfun Sonmez & M. Utku Unver, 2003. "Kidney Exchange," NBER Working Papers 10002, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  5. Robert Wilson, 2002. "Architecture of Power Markets," Econometrica, Econometric Society, vol. 70(4), pages 1299-1340, July. [Downloadable!] (restricted)
  6. Alvin E. Roth & Axel Ockenfels, 2002. "Last-Minute Bidding and the Rules for Ending Second-Price Auctions: Evidence from eBay and Amazon Auctions on the Internet," American Economic Review, American Economic Association, vol. 92(4), pages 1093-1103, September. [Downloadable!]
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  7. 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. [Downloadable!] (restricted)
  8. Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," Econometrica, Econometric Society, vol. 70(4), pages 1341-1378, July. [Downloadable!] (restricted)
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  1. Leufkens, Kasper & Peeters, Ronald, 2008. "Price dynamics and collusion under short-run price commitments," Research Memoranda 052, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  2. Howard Kunreuther & Gabriel Silvasi & Eric T. Bradlow & Dylan Small, 2007. "Deterministic and Stochastic Prisoner's Dilemma Games: Experiments in Interdependent Security," NBER Technical Working Papers 0341, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  3. Howard Kunreuther & Gabriel Silvasi & Eric T. Bradlow & Dylan Small, 2009. "Bayesian analysis of deterministic and stochastic prisoner's dilemma games," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 4(5), pages 363-384, August. [Downloadable!]
  4. Pedro Dal Bo & Guillaume R. Frechette, . "The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence," Working Papers 2007-7, Brown University, Department of Economics. [Downloadable!]
  5. Pedro Dal Bó & Andrew Foster & Louis Putterman, 2008. "Institutions and Behavior: Experimental Evidence on the Effects of Democracy," NBER Working Papers 13999, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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