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A Behavioral Foundation for Models of Evolutionary Drift

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  • Uriarte Ayo, José Ramón

Abstract

Binmore and Samuelson (1999) have shown that perturbations (drift) are crucial to study the stability properties of Nash equilibria. We contribute to this literature by providing a behavioural foundation for models of evolutionary drift. In particular, this article introduces a microeconomic model of drift based on the similarity theory developed by Tversky (1977), Kahneman and Tversky (1979) and Rubinstein (1988),(1998). An innovation with respect to those works is that we deal with similarity relations that are derived from the perception that each agent has about how well he is playing the game. In addition, the similarity relations are adapted to a dynamic setting. We obtain different models of drift depending on how we model the agent´s assessment of his behaviour in the game. The examples of the ultimatum game and the chain-store game are used to show the conditions for each model to stabilize elements in the component of Nash equilibria that are not subgame- perfect. It is also shown how some models approximate the laboratory data about those games while others match the data.

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Bibliographic Info

Paper provided by Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I in its series IKERLANAK with number 2005-19.

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Date of creation: Jul 2005
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Handle: RePEc:ehu:ikerla:200519

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Postal: Dpto. de Fundamentos del Análisis Económico I, Facultad de CC. Económicas y Empresariales, Universidad del País Vasco, Avda. Lehendakari Aguirre 83, 48015 Bilbao, Spain
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Keywords: similarity relations; drift; Nash equilibrium; selection dynamics; learning;

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References

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  1. Binmore, Ken & Samuelson, Larry, 1999. "Evolutionary Drift and Equilibrium Selection," Review of Economic Studies, Wiley Blackwell, vol. 66(2), pages 363-93, April.
  2. Antonio Cabrales, 1993. "Stochastic replicator dynamics," Economics Working Papers 54, Department of Economics and Business, Universitat Pompeu Fabra.
  3. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer, vol. 1(1), pages 9-41, June.
  4. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  5. Tilman B�rgers & Rajiv Sarin, . "Learning Through Reinforcement and Replicator Dynamics," ELSE working papers 051, ESRC Centre on Economics Learning and Social Evolution.
  6. Guth, Werner & Huck, Steffen & Muller, Wieland, 2001. "The Relevance of Equal Splits in Ultimatum Games," Games and Economic Behavior, Elsevier, vol. 37(1), pages 161-169, October.
  7. Schotter Andrew & Weigelt Keith & Wilson Charles, 1994. "A Laboratory Investigation of Multiperson Rationality and Presentation Effects," Games and Economic Behavior, Elsevier, vol. 6(3), pages 445-468, May.
  8. Larry Samuelson, 1998. "Evolutionary Games and Equilibrium Selection," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262692198, January.
  9. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
  10. Ed Hopkins, 2001. "Two Competing Models of How People Learn in Games," NajEcon Working Paper Reviews 625018000000000226, www.najecon.org.
  11. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
  12. Abbink, Klaus & Gary Bolton & Abdolkarim Sadrieh & Fang-Fang Tang, 1996. "Adaptive Learning versus Punishment in Ultimatum Bargaining," Discussion Paper Serie B 381, University of Bonn, Germany.
  13. repec:att:wimass:9325 is not listed on IDEAS
  14. Binmore,K. & McCarthy,J. & Ponti,G. & ..., 1999. "A backward induction experiment," Working papers 34, Wisconsin Madison - Social Systems.
  15. Roth, Alvin E. & Vesna Prasnikar & Masahiro Okuno-Fujiwara & Shmuel Zamir, 1991. "Bargaining and Market Behavior in Jerusalem, Ljubljana, Pittsburgh, and Tokyo: An Experimental Study," American Economic Review, American Economic Association, vol. 81(5), pages 1068-95, December.
  16. Rubinstein, Ariel, 1988. "Similarity and decision-making under risk (is there a utility theory resolution to the Allais paradox?)," Journal of Economic Theory, Elsevier, vol. 46(1), pages 145-153, October.
  17. Aizpurua, J M, et al, 1993. " Similarity and Preferences in the Space of Simple Lotteries," Journal of Risk and Uncertainty, Springer, vol. 6(3), pages 289-97, June.
  18. H. Peyton Young, 1996. "The Economics of Convention," Journal of Economic Perspectives, American Economic Association, vol. 10(2), pages 105-122, Spring.
  19. Cheung, Yin-Wong & Friedman, Daniel, 1998. "A comparison of learning and replicator dynamics using experimental data," Journal of Economic Behavior & Organization, Elsevier, vol. 35(3), pages 263-280, April.
  20. JosÊ RamÕn Uriarte, 1999. "Decision-making under risk: Editing procedures based on correlated similarities, and preference overdetermination," Review of Economic Design, Springer, vol. 4(1), pages 1-12.
  21. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
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Cited by:
  1. Iriberri, Nagore & Uriarte Ayo, José Ramón, 2006. "The Language Game: A Game-Theoretic Approach to Language Contact," IKERLANAK 2006-24, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
  2. Cabrales, Antonio & Uriarte Ayo, José Ramón, 2007. "Doubts and Equilibria," IKERLANAK 2008-31, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.

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