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A Behavioral Foundation for Models of Evolutionary Drift

  • Uriarte Ayo, José Ramón

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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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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Order Information: 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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  1. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  2. 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.
  3. 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.
  4. 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.
  5. Larry Samuelson, 1998. "Evolutionary Games and Equilibrium Selection," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262692198, June.
  6. Alvin E. Roth & V. Prasnikar & M. Okuno-Fujiwara & S. Zamir, 1998. "Bargaining and market behavior in Jerusalem, Liubljana, Pittsburgh and Tokyo: an experimental study," Levine's Working Paper Archive 344, David K. Levine.
  7. Binmore,K. & McCarthy,J. & Ponti,G. & ..., 1999. "A backward induction experiment," Working papers 34, Wisconsin Madison - Social Systems.
  8. Karl H. Schlag, . "Why Imitate, and if so, How? A Bounded Rational Approach to Multi- Armed Bandits," ELSE working papers 028, ESRC Centre on Economics Learning and Social Evolution.
  9. A. Cabrales, 2010. "Stochastic Replicator Dynamics," Levine's Working Paper Archive 489, David K. Levine.
  10. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
  11. Young H. P., 1993. "An Evolutionary Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 59(1), pages 145-168, February.
  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. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer, vol. 1(1), pages 9-41, June.
  14. Ed Hopkins, 2001. "Two Competing Models of How People Learn in Games," NajEcon Working Paper Reviews 625018000000000226, www.najecon.org.
  15. 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.
  16. repec:att:wimass:9325 is not listed on IDEAS
  17. Binmore, Ken & Samuelson, Larry, 1999. "Evolutionary Drift and Equilibrium Selection," Review of Economic Studies, Wiley Blackwell, vol. 66(2), pages 363-93, April.
  18. 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.
  19. 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.
  20. 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.
  21. H. Peyton Young, 1996. "The Economics of Convention," Journal of Economic Perspectives, American Economic Association, vol. 10(2), pages 105-122, Spring.
  22. 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.
  23. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
  24. Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B 296, University of Bonn, Germany.
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