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A numerical analysis of the evolutionary stability of learning rules

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  • Josephson, Jens

Abstract

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

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  1. 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.
  2. Drew Fudenberg & David K. Levine, 1996. "The Theory of Learning in Games," Levine's Working Paper Archive 624, David K. Levine.
  3. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186 Elsevier.
  4. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
  5. Ed Hopkins & Martin Posch, 2004. "Attainability of Boundary Points under Reinforcement Learning," ESE Discussion Papers 79, Edinburgh School of Economics, University of Edinburgh.
  6. Hanaki, Nobuyuki & Sethi, Rajiv & Erev, Ido & Peterhansl, Alexander, 2005. "Learning strategies," Journal of Economic Behavior & Organization, Elsevier, vol. 56(4), pages 523-542, April.
  7. Ed Hopkins, . "Learning, Matching and Aggregation," ESE Discussion Papers 2, Edinburgh School of Economics, University of Edinburgh.
  8. Anderlini, L & Sabourian, H, 1996. "The Evolution of Algorithmic Learning Rules : A Global Stability Result," Economics Working Papers eco96/05, European University Institute.
  9. 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.
  10. Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, vol. 122(1), pages 1-36, May.
  11. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
  12. Timothy C. Salmon, 2001. "An Evaluation of Econometric Models of Adaptive Learning," Econometrica, Econometric Society, vol. 69(6), pages 1597-1628, November.
  13. 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.
  14. Arthur J. Robson, 2001. "The Biological Basis of Economic Behavior," Journal of Economic Literature, American Economic Association, vol. 39(1), pages 11-33, March.
  15. Nathaniel T Wilcox, 2006. "Theories of Learning in Games and Heterogeneity Bias," Econometrica, Econometric Society, vol. 74(5), pages 1271-1292, 09.
  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. Heller, Dana, 2004. "An evolutionary approach to learning in a changing environment," Journal of Economic Theory, Elsevier, vol. 114(1), pages 31-55, January.
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Cited by:
  1. Hanaki, Nobuyuki & Ishikawa, Ryuichiro & Akiyama, Eizo, 2009. "Learning games," Journal of Economic Dynamics and Control, Elsevier, vol. 33(10), pages 1739-1756, October.
  2. Josephson, Jens, 2001. "Stochastic Adaptation in Finite Games Played by Heterogeneous Populations," Working Paper Series in Economics and Finance 475, Stockholm School of Economics.
  3. 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.
  4. Mohlin, Erik, 2010. "Evolution of Theories of Mind," Working Paper Series in Economics and Finance 0728, Stockholm School of Economics, revised 12 May 2010.
  5. Jurjen Kamphorst & Gerard van der Laan, 2006. "Learning in a Local Interaction Hawk-Dove Game," Tinbergen Institute Discussion Papers 06-034/1, Tinbergen Institute.
  6. Matros, Alexander, 2012. "Altruistic versus egoistic behavior in a Public Good game," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 642-656.
  7. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2012. "Once Beaten, Never Again: Imitation in Two-Player Potential Games," Working Papers 0529, University of Heidelberg, Department of Economics.

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