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Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits

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  • Schlag, Karl H.

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 pay-off s for any underlying payoff distribution. It is shown that the rule that outperforms all other rules with this property is the one that specifies imita-tion 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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 78 (1998)
Issue (Month): 1 (January)
Pages: 130-156

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Handle: RePEc:eee:jetheo:v:78:y:1998:i:1:p:130-156

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Web page: http://www.elsevier.com/locate/inca/622869

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  1. Robson, Arthur J., 1996. "A Biological Basis for Expected and Non-expected Utility," Journal of Economic Theory, Elsevier, vol. 68(2), pages 397-424, February.
  2. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
  3. Cabrales, Antonio, 2000. "Stochastic Replicator Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(2), pages 451-81, May.
  4. Fudenberg, Drew & Ellison, Glenn, 1995. "Word-of-Mouth Communication and Social Learning," Scholarly Articles 3196300, Harvard University Department of Economics.
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  8. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  9. Karl H. Schlag, . "Why Imitate, and if so, How? A Bounded Rational Approach to Multi- Armed Bandits," ELSE working papers 028, ESRC Centre on Economics Learning and Social Evolution.
  10. Binmore Kenneth G. & Samuelson Larry & Vaughan Richard, 1995. "Musical Chairs: Modeling Noisy Evolution," Games and Economic Behavior, Elsevier, vol. 11(1), pages 1-35, October.
  11. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
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  13. Schlag, Karl H., 1999. "Which one should I imitate?," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 493-522, May.
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  16. 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.
  17. Dan Friedman, 2010. "Evolutionary Games in Economics," Levine's Working Paper Archive 392, David K. Levine.
  18. L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, David K. Levine.
  19. Helbing, Dirk, 1992. "Interrelations between stochastic equations for systems with pair interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 181(1), pages 29-52.
  20. Jonas Bjoernerstedt & Karl H. Schlag, . "On the Evolution of Imitative Behavior," ELSE working papers 029, ESRC Centre on Economics Learning and Social Evolution.
  21. repec:att:wimass:9325 is not listed on IDEAS
  22. Cross, John G, 1973. "A Stochastic Learning Model of Economic Behavior," The Quarterly Journal of Economics, MIT Press, vol. 87(2), pages 239-66, May.
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  26. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
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