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

  • Karl H. Schlag

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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Paper provided by ESRC Centre on Economics Learning and Social Evolution in its series ELSE working papers with number 028.

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Handle: RePEc:els:esrcls:028
Contact details of provider: Web page: http://else.econ.ucl.ac.uk/
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  1. Jonas Bjoernerstedt & Karl H. Schlag, . "On the Evolution of Imitative Behavior," ELSE working papers 029, ESRC Centre on Economics Learning and Social Evolution.
  2. repec:att:wimass:9325 is not listed on IDEAS
  3. Karl H. Schlag, 1995. "Why Imitate, and if so, How? A Bounded Rational Approach to Multi-Armed Bandits," Discussion Paper Serie B 361, University of Bonn, Germany, revised Mar 1996.
  4. 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.
  5. 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.
  6. Bjornerstedt, J. & Weibull, J.W., 1993. "Nash Equilibrium and Evolution by Imitation," DELTA Working Papers 93-23, DELTA (Ecole normale supérieure).
  7. Tilman B�rgers & Rajiv Sarin, . "Learning Through Reinforcement and Replicator Dynamics," ELSE working papers 051, ESRC Centre on Economics Learning and Social Evolution.
  8. 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.
  9. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
  10. David Easley & Aldo Rustichini, 1999. "Choice without Beliefs," Econometrica, Econometric Society, vol. 67(5), pages 1157-1184, September.
  11. Antonio Cabrales, 1993. "Stochastic replicator dynamics," Economics Working Papers 54, Department of Economics and Business, Universitat Pompeu Fabra.
  12. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
  13. 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.
  14. 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.
  15. 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.
  16. L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, David K. Levine.
  17. 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.
  18. Samuelson, L. & Zhang, J., 1991. "Evolutionary Stability in Asymmetric Games," Papers 9132, Tilburg - Center for Economic Research.
  19. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
  20. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  21. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
  22. Boylan, Richard T., 1992. "Laws of large numbers for dynamical systems with randomly matched individuals," Journal of Economic Theory, Elsevier, vol. 57(2), pages 473-504, August.
  23. Schlag, Karl H., 1999. "Which one should I imitate?," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 493-522, May.
  24. Dan Friedman, 2010. "Evolutionary Games in Economics," Levine's Working Paper Archive 392, David K. Levine.
  25. Banerjee, Abhijit V, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, MIT Press, vol. 107(3), pages 797-817, August.
  26. Schmalensee, Richard, 1975. "Alternative models of bandit selection," Journal of Economic Theory, Elsevier, vol. 10(3), pages 333-342, June.
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