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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 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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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. Björnerstedt, Jonas & Weibull, Jörgen W., 1994. "Nash Equilibrium and Evolution by Imitation," Working Paper Series, Research Institute of Industrial Economics 407, Research Institute of Industrial Economics.
  2. Björnerstedt, Jonas & Karl H. Schlag, 1996. "On the Evolution of Imitative Behavior," Discussion Paper Serie B 378, University of Bonn, Germany.
  3. Dan Friedman, 2010. "Evolutionary Games in Economics," Levine's Working Paper Archive 392, David K. Levine.
  4. A. Banerjee & Drew Fudenberg, 2010. "Word-of-Mouth Communication and Social Learning," Levine's Working Paper Archive 425, David K. Levine.
  5. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, Elsevier, vol. 9(2), pages 185-202, October.
  6. A. Cabrales, 2010. "Stochastic Replicator Dynamics," Levine's Working Paper Archive 489, David K. Levine.
  7. Samuelson, L. & Zhang, J., 1991. "Evolutionary Stability in Asymmetric Games," Papers, Tilburg - Center for Economic Research 9132, Tilburg - Center for Economic Research.
  8. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, Elsevier, vol. 57(2), pages 363-391, August.
  9. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  10. L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, David K. Levine.
  11. 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.
  12. 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.
  13. Banerjee, Abhijit V, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 107(3), pages 797-817, August.
  14. T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
  15. Robson, Arthur J., 1996. "A Biological Basis for Expected and Non-expected Utility," Journal of Economic Theory, Elsevier, Elsevier, vol. 68(2), pages 397-424, February.
  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. Boylan, Richard T., 1992. "Laws of large numbers for dynamical systems with randomly matched individuals," Journal of Economic Theory, Elsevier, Elsevier, vol. 57(2), pages 473-504, August.
  18. Schmalensee, Richard, 1975. "Alternative models of bandit selection," Journal of Economic Theory, Elsevier, Elsevier, vol. 10(3), pages 333-342, June.
  19. Cross, John G, 1973. "A Stochastic Learning Model of Economic Behavior," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 87(2), pages 239-66, May.
  20. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, Elsevier, vol. 57(2), pages 343-362, August.
  21. 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.
  22. Schlag, Karl H., 1996. "Which one should I imitate?," Discussion Paper Serie B 365, University of Bonn, Germany.
  23. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, Econometric Society, vol. 59(3), pages 637-66, May.
  24. Helbing, Dirk, 1992. "Interrelations between stochastic equations for systems with pair interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 181(1), pages 29-52.
  25. repec:att:wimass:9325 is not listed on IDEAS
  26. David Easley & Aldo Rustichini, 1999. "Choice without Beliefs," Econometrica, Econometric Society, Econometric Society, vol. 67(5), pages 1157-1184, September.
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