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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. 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.
  2. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
  3. Abhijit V. Banerjee, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, Oxford University Press, vol. 107(3), pages 797-817.
  4. 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.
  5. Schmalensee, Richard, 1975. "Alternative models of bandit selection," Journal of Economic Theory, Elsevier, vol. 10(3), pages 333-342, June.
  6. Schlag, Karl H., 1999. "Which one should I imitate?," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 493-522, May.
  7. T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
  8. Antonio Cabrales, 1993. "Stochastic replicator dynamics," Economics Working Papers 54, Department of Economics and Business, Universitat Pompeu Fabra.
  9. Glenn Ellison & Drew Fudenberg, 1995. "Word-of-Mouth Communication and Social Learning," The Quarterly Journal of Economics, Oxford University Press, vol. 110(1), pages 93-125.
  10. 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.
  11. Björnerstedt, Jonas & Karl H. Schlag, 1996. "On the Evolution of Imitative Behavior," Discussion Paper Serie B 378, University of Bonn, Germany.
  12. 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.
  13. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  14. Samuelson, L. & Zhang, J., 1990. "Evolutionary Stability In Symmetric Games," Working papers 90-24, Wisconsin Madison - Social Systems.
  15. Björnerstedt, Jonas & Weibull, Jörgen W., 1994. "Nash Equilibrium and Evolution by Imitation," Working Paper Series 407, Research Institute of Industrial Economics.
  16. 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.
  17. A. Banerjee & Drew Fudenberg, 2010. "Word-of-Mouth Communication and Social Learning," Levine's Working Paper Archive 425, David K. Levine.
  18. Rothschild, Michael, 1974. "A two-armed bandit theory of market pricing," Journal of Economic Theory, Elsevier, vol. 9(2), pages 185-202, October.
  19. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-66, May.
  20. John G. Cross, 1973. "A Stochastic Learning Model of Economic Behavior," The Quarterly Journal of Economics, Oxford University Press, vol. 87(2), pages 239-266.
  21. David Easley & Aldo Rustichini, 1999. "Choice without Beliefs," Econometrica, Econometric Society, vol. 67(5), pages 1157-1184, September.
  22. 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.
  23. Dan Friedman, 2010. "Evolutionary Games in Economics," Levine's Working Paper Archive 392, David K. Levine.
  24. 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.
  25. repec:att:wimass:9325 is not listed on IDEAS
  26. L. Samuelson & J. Zhang, 2010. "Evolutionary Stability in Asymmetric Games," Levine's Working Paper Archive 453, David K. Levine.
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