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A Numerical Analysis of the Evolutionary Stability of Learning Rules

  • Josephson, Jens


    (Dept. of Economics, Stockholm School of Economics)

In this paper I define an evolutionary stability criterion for learning rules. Using Monte Carlo simulations, I then apply this criterion to a class of learning rules that can be represented by Camerer and Ho's (1999) model of learning. This class contains perturbed versions of reinforcement and belief learning as special cases. A large population of individuals with learning rules in this class are repeatedly rematched for a finite number of periods and play one out of four symmetric two-player games. Belief learning is the only learning rule which is evolutionarily stable in almost all cases, whereas reinforcement learning is unstable in almost all cases. I also find that in certain games, the stability of intermediate learning rules hinges critically on a parameter of the model and the relative payoffs.

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Paper provided by Stockholm School of Economics in its series SSE/EFI Working Paper Series in Economics and Finance with number 474.

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Length: 29 pages
Date of creation: 15 Nov 2001
Date of revision:
Handle: RePEc:hhs:hastef:0474
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  1. Cars H. Hommes, 2005. "Heterogeneous Agent Models in Economics and Finance," Tinbergen Institute Discussion Papers 05-056/1, Tinbergen Institute.
  2. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
  3. Timothy C. Salmon, 2001. "An Evaluation of Econometric Models of Adaptive Learning," Econometrica, Econometric Society, vol. 69(6), pages 1597-1628, November.
  4. Ed Hopkins & Martin Posch, 2003. "Attainability of Boundary Points under Reinforcement Learning," ESE Discussion Papers 79, Edinburgh School of Economics, University of Edinburgh.
  5. Ed Hopkins, . "Learning, Matching and Aggregation," ELSE working papers 033, ESRC Centre on Economics Learning and Social Evolution.
  6. Camerer, Colin F. & Ho, Teck-Hua & Chong, Juin-Kuan, 2002. "Sophisticated Experience-Weighted Attraction Learning and Strategic Teaching in Repeated Games," Journal of Economic Theory, Elsevier, vol. 104(1), pages 137-188, May.
  7. Anderlini, L & Sabourian, H, 1996. "The Evolution of Algorithmic Learning Rules : A Global Stability Result," Economics Working Papers eco96/05, European University Institute.
  8. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, June.
  9. Alan Beggs, 2002. "On the Convergence of Reinforcement Learning," Economics Series Working Papers 96, University of Oxford, Department of Economics.
  10. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
  11. Nathaniel T Wilcox, 2006. "Theories of Learning in Games and Heterogeneity Bias," Econometrica, Econometric Society, vol. 74(5), pages 1271-1292, 09.
  12. Arthur J. Robson, 2001. "The Biological Basis of Economic Behavior," Journal of Economic Literature, American Economic Association, vol. 39(1), pages 11-33, March.
  13. Heller, Dana, 2004. "An evolutionary approach to learning in a changing environment," Journal of Economic Theory, Elsevier, vol. 114(1), pages 31-55, January.
  14. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-81, September.
  15. Teck H Ho & Colin Camerer & Juin-Kuan Chong, 2003. "Functional EWA: A one-parameter theory of learning in games," Levine's Working Paper Archive 506439000000000514, David K. Levine.
  16. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
  17. Nobuyuki Hanaki & Rajiv Sethi & Ido Erev & Alexander Peterhansl, 2002. "Learning Strategies," Game Theory and Information 0211004, EconWPA.
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