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

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  • Karl H. Schlag

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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File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonsfb/bonsfb361.pdf
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Bibliographic 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

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Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de

Related research

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

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  1. Bjornerstedt, J. & Weibull, J.W., 1993. "Nash Equilibrium and Evolution by Imitation," DELTA Working Papers, DELTA (Ecole normale supérieure) 93-23, DELTA (Ecole normale supérieure).
  2. 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.
  3. Antonio Cabrales, 1993. "Stochastic replicator dynamics," Economics Working Papers 54, Department of Economics and Business, Universitat Pompeu Fabra.
  4. Schlag, Karl H., 1996. "Which one should I imitate?," Discussion Paper Serie B, University of Bonn, Germany 365, University of Bonn, Germany.
  5. K. Schlag, 2010. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Levine's Working Paper Archive 454, David K. Levine.
  6. T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
  7. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, Elsevier, vol. 78(1), pages 130-156, January.
  8. Samuelson, L., 1989. "Evolutionnary Stability In Asymmetric Games," Papers, Pennsylvania State - Department of Economics 11-8-2, Pennsylvania State - Department of Economics.
  9. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, Econometric Society, vol. 59(3), pages 637-66, May.
  10. Ellison, Glenn & Fudenberg, Drew, 1995. "Word-of-Mouth Communication and Social Learning," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 110(1), pages 93-125, February.
  11. 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.
  12. Dan Friedman, 2010. "Evolutionary Games in Economics," Levine's Working Paper Archive 392, David K. Levine.
  13. 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.
  14. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  15. 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.
  16. Jonas Bjoernerstedt & Karl H. Schlag, . "On the Evolution of Imitative Behavior," ELSE working papers, ESRC Centre on Economics Learning and Social Evolution 029, ESRC Centre on Economics Learning and Social Evolution.
  17. Binmore Kenneth G. & Samuelson Larry & Vaughan Richard, 1995. "Musical Chairs: Modeling Noisy Evolution," Games and Economic Behavior, Elsevier, Elsevier, vol. 11(1), pages 1-35, October.
  18. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, Elsevier, vol. 9(2), pages 185-202, October.
  19. Schmalensee, Richard, 1975. "Alternative models of bandit selection," Journal of Economic Theory, Elsevier, Elsevier, vol. 10(3), pages 333-342, June.
  20. L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, David K. Levine.
  21. repec:att:wimass:9325 is not listed on IDEAS
  22. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, Elsevier, vol. 57(2), pages 363-391, August.
  23. 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.
  24. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, Elsevier, vol. 57(2), pages 343-362, August.
  25. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, Elsevier, vol. 8(1), pages 56-90.
  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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