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

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Author Info
Karl H. Schlag

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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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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

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

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

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  1. Samuelson, L. & Zhang, J., 1991. "Evolutionary Stability in Asymmetric Games," Papers 9132, Tilburg - Center for Economic Research.
    Other versions:
  2. 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. [Downloadable!]
    Other versions:
  3. Schlag, Karl H., 1999. "Which one should I imitate?," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 493-522, May. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  5. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August. [Downloadable!] (restricted)
  6. repec:att:wimass:199325 is not listed on IDEAS
  7. Björnerstedt, Jonas, and Karl H. Schlag, 1996. "On the Evolution of Imitative Behavior," Discussion Paper Serie B 378, University of Bonn, Germany. [Downloadable!]
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  8. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August. [Downloadable!] (restricted)
  9. Banerjee, Abhijit V, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, MIT Press, vol. 107(3), pages 797-817, August. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Alan Beggs, 2000. "Stochastic Evolution with Slow Learning," Economics Series Working Papers 033, University of Oxford, Department of Economics. [Downloadable!]
    Other versions:
  2. Cartwright, Edward, 2003. "Learning To Play Approximate Nash Equilibria In Games With Many Players," The Warwick Economics Research Paper Series (TWERPS) 671, University of Warwick, Department of Economics. [Downloadable!]
    Other versions:
  3. Jorg Oechssler & Karl Schlag, 1997. "An Evolutionary Analysis of Bagwell's Example," Game Theory and Information 9704001, EconWPA, revised 11 Apr 1997. [Downloadable!]
  4. Tilman Slembeck, 2000. "Learning in Economics: Where Do We Stand?," Microeconomics 0004007, EconWPA. [Downloadable!]
  5. Gerard van der Laan & A.F. Tieman, 1996. "Evolutionary Game Theory and the Modelling of Economic Behavior," Tinbergen Institute Discussion Papers 96-172/8, Tinbergen Institute. [Downloadable!]
  6. Fernando Vega-Redondo, 1999. "Markets under bounded rationality: from theory to facts," Investigaciones Economicas, Fundación SEPI, vol. 23(1), pages 3-26, January. [Downloadable!]
  7. Tilman Borgers & Antonio Morales & Rajiv Sarin, 2003. "Expedient and Monotone Learning Rules," Levine's Bibliography 625018000000000099, UCLA Department of Economics. [Downloadable!]
    Other versions:
  8. Droste, E. & Tuinstra, J., 1998. "Evolutionary selection of behavioral rules in a Cournot model : a local bifurcation analysis," Discussion Paper 86, Tilburg University, Center for Economic Research. [Downloadable!]
  9. Antonio Cabrales & Giovanni Ponti, 2000. "Implementation, Elimination of Weakly Dominated Strategies and Evolutionary Dynamics," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(2), pages 247-282, April. [Downloadable!] (restricted)
    Other versions:
  10. Ulrich Berger, 2003. "A general model of best response adaptation," Game Theory and Information 0303008, EconWPA. [Downloadable!]
  11. Weibull, Jörgen W., 1997. "What have we learned from Evolutionary Game Theory so far?," Working Paper Series 487, Research Institute of Industrial Economics, revised 26 Oct 1998. [Downloadable!]
    Other versions:
  12. Burkhard C. Schipper, 2005. "Imitators and Optimizers in Cournot Oligopoly," Discussion Papers 53, SFB/TR 15 Governance and the Efficiency of Economic Systems, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich. [Downloadable!]
    Other versions:
  13. Cartwright, Edward, 2003. "Imitation and the Emergence of Nash Equilibrium Play in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS) 684, University of Warwick, Department of Economics. [Downloadable!]
  14. Alexander F. Tieman & Harold Houba & Gerard van der Laan, 1998. "Cooperation in a Multi-Dimensional Local Interaction Model," Game Theory and Information 9803002, EconWPA. [Downloadable!]
    Other versions:
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