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Why Imitate, and if so, How? A Bounded Rational Approach to Multi-Armed Bandits

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Author Info
Karl H. Schlag

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Abstract

We consider the situation in which individuals in a finite population must repeatedly choose an action yielding an uncertain payoff. Between choices, each individual may observe the performance of one other individual. We search for rules of behavior with limited memory that increase expected payoffs for any underlying payoff distribution. It is shown that the rule that outperforms all other rules with this property is the one that specifies imitation of the action of an individual that performed better with a probability proportional to how much better she performed. When each individual uses this best rule, the aggregate population behavior can be approximated by the replicator dynamic.

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Publisher Info
Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 361.

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Length: pages
Date of creation: Dec 1995
Date of revision: Mar 1996
Handle: RePEc:bon:bonsfb:361

Contact details of provider:
Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 9221
Web page: http://www.bgse.uni-bonn.de/index.php?id=517

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Related research
Keywords: social learning bounded rationality imitation multi-armed bandit random matching payoff increasing replicator dynamic.

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

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. Björnerstedt, Jonas, and Karl H. Schlag, 1996. "On the Evolution of Imitative Behavior," Discussion Paper Serie B 378, University of Bonn, Germany. [Downloadable!]
    Other versions:
  2. Samuelson, L. & Zhang, J., 1991. "Evolutionary Stability in Asymmetric Games," Papers 9132, Tilburg - Center for Economic Research.
    Other versions:
  3. Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B 296, University of Bonn, Germany. [Downloadable!]
    Other versions:
  4. Schlag, Karl H., 1999. "Which one should I imitate?," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 493-522, May. [Downloadable!] (restricted)
  5. Ellison, Glenn & Fudenberg, Drew, 1995. "Word-of-Mouth Communication and Social Learning," The Quarterly Journal of Economics, MIT Press, vol. 110(1), pages 93-125, February. [Downloadable!] (restricted)
  6. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August. [Downloadable!] (restricted)
  7. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August. [Downloadable!] (restricted)
  8. Banerjee, Abhijit V, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, MIT Press, vol. 107(3), pages 797-817, August. [Downloadable!] (restricted)
  9. repec:att:wimass:199325 is not listed on IDEAS
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