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A Numerical Analysis of the Evolutionary Stability of Learning Rules

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  • Josephson, Jens

    ()
    (Dept. of Economics, Stockholm School of Economics)

Abstract

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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Bibliographic Info

Paper provided by Stockholm School of Economics in its series 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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Web page: http://www.hhs.se/
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Keywords: Bounded rationality; Evolutionary game theory; Evolutionary Stability; Learning in games; Belief learning; Reinforcement learning.;

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References

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  1. Ed Hopkins, 2001. "Two Competing Models of How People Learn in Games," Levine's Working Paper Archive 625018000000000226, David K. Levine.
  2. Hopkins, E., 1995. "Learning, Matching and Aggregation," G.R.E.Q.A.M., Universite Aix-Marseille III 95a20, Universite Aix-Marseille III.
  3. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  4. Hanaki, Nobuyuki & Sethi, Rajiv & Erev, Ido & Peterhansl, Alexander, 2005. "Learning strategies," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 56(4), pages 523-542, April.
  5. 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.
  6. Heller, Dana, 2004. "An evolutionary approach to learning in a changing environment," Journal of Economic Theory, Elsevier, Elsevier, vol. 114(1), pages 31-55, January.
  7. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, Econometric Society, vol. 70(6), pages 2265-2294, November.
  8. Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, Elsevier, vol. 122(1), pages 1-36, May.
  9. Cars H. Hommes, 2005. "Heterogeneous Agent Models in Economics and Finance," Tinbergen Institute Discussion Papers, Tinbergen Institute 05-056/1, Tinbergen Institute.
  10. Arthur J. Robson, 2001. "The Biological Basis of Economic Behavior," Journal of Economic Literature, American Economic Association, American Economic Association, vol. 39(1), pages 11-33, March.
  11. Anderlini, L & Sabourian, H, 1996. "The Evolution of Algorithmic Learning Rules : A Global Stability Result," Economics Working Papers, European University Institute eco96/05, European University Institute.
  12. 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, Elsevier, vol. 104(1), pages 137-188, May.
  13. Ed Hopkins & Martin Posch, 2003. "Attainability of Boundary Points under Reinforcement Learning," Levine's Working Paper Archive 506439000000000350, David K. Levine.
  14. Timothy C. Salmon, 2001. "An Evaluation of Econometric Models of Adaptive Learning," Econometrica, Econometric Society, Econometric Society, vol. 69(6), pages 1597-1628, November.
  15. 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, American Economic Association, vol. 88(4), pages 848-81, September.
  16. Nathaniel T Wilcox, 2006. "Theories of Learning in Games and Heterogeneity Bias," Econometrica, Econometric Society, Econometric Society, vol. 74(5), pages 1271-1292, 09.
  17. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, Econometric Society, vol. 67(4), pages 827-874, July.
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Citations

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Cited by:
  1. Josephson, Jens, 2001. "Stochastic Adaptation in Finite Games Played by Heterogeneous Populations," Working Paper Series in Economics and Finance, Stockholm School of Economics 475, Stockholm School of Economics.
  2. Jurjen Kamphorst & Gerard van der Laan, 2006. "Learning in a Local Interaction Hawk-Dove Game," Tinbergen Institute Discussion Papers, Tinbergen Institute 06-034/1, Tinbergen Institute.
  3. Hanaki, Nobuyuki & Ishikawa, Ryuichiro & Akiyama, Eizo, 2009. "Learning games," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 33(10), pages 1739-1756, October.
  4. Mohlin, Erik, 2012. "Evolution of theories of mind," Games and Economic Behavior, Elsevier, Elsevier, vol. 75(1), pages 299-318.
  5. Peter Duersch & Joerg Oechssler & Burkhard Schipper, 2011. "Once Beaten, Never Again: Imitation in Two-Player Potential Games," Working Papers, University of California, Davis, Department of Economics 1112, University of California, Davis, Department of Economics.
  6. Matros, Alexander, 2012. "Altruistic versus egoistic behavior in a Public Good game," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 36(4), pages 642-656.
  7. 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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