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A numerical analysis of the evolutionary stability of learning rules

  • Josephson, Jens

In this paper, we define an evolutionary stability criterion for learning rules. Using simulations, we then apply this criterion to three types of symmetric 2x2 games for a class of learning rules that can be represented by the parametric model of Camerer and Ho [1999. Experience-weighted attraction learning in normal form games. Econometrica 67, 827-874]. This class contains stochastic versions of reinforcement and fictitious play as extreme cases. We find that only learning rules with high or intermediate levels of hypothetical reinforcement are evolutionarily stable, but that the stable parameters depend on the game.

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Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 32 (2008)
Issue (Month): 5 (May)
Pages: 1569-1599

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Handle: RePEc:eee:dyncon:v:32:y:2008:i:5:p:1569-1599
Contact details of provider: Web page: http://www.elsevier.com/locate/jedc

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  1. Arthur J. Robson, 2001. "The Biological Basis of Economic Behavior," Journal of Economic Literature, American Economic Association, vol. 39(1), pages 11-33, March.
  2. Cars H. Hommes, 2005. "Heterogeneous Agent Models in Economics and Finance," Tinbergen Institute Discussion Papers 05-056/1, Tinbergen Institute.
  3. Ed Hopkins, . "Learning, Matching and Aggregation," ELSE working papers 033, ESRC Centre on Economics Learning and Social Evolution.
  4. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
  5. 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.
  6. Nobuyuki Hanaki & Rajiv Sethi & Ido Erev & Alexander Peterhansl, 2002. "Learning Strategies," Game Theory and Information 0211004, EconWPA.
  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. Ed Hopkins, 2000. "Two Competing Models of How People Learn in Games," ESE Discussion Papers 51, Edinburgh School of Economics, University of Edinburgh.
  9. 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.
  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. Hopkins, Ed & Posch, Martin, 2005. "Attainability of boundary points under reinforcement learning," Games and Economic Behavior, Elsevier, vol. 53(1), pages 110-125, October.
  12. Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, vol. 122(1), pages 1-36, May.
  13. Nathaniel T Wilcox, 2006. "Theories of Learning in Games and Heterogeneity Bias," Econometrica, Econometric Society, vol. 74(5), pages 1271-1292, 09.
  14. Timothy C. Salmon, 2001. "An Evaluation of Econometric Models of Adaptive Learning," Econometrica, Econometric Society, vol. 69(6), pages 1597-1628, November.
  15. Heller, Dana, 2004. "An evolutionary approach to learning in a changing environment," Journal of Economic Theory, Elsevier, vol. 114(1), pages 31-55, January.
  16. 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.
  17. 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.
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