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Doubts and Equilibria

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  • Cabrales, Antonio
  • Uriarte Ayo, José Ramón

Abstract

In real life strategic interactions, decision-makers are likely to entertain doubts about the degree of optimality of their play. To capture this feature of real choice-making, we present here a model based on the doubts felt by an agent about how well is playing a game. The doubts are coupled with (and mutually reinforced by) imperfect discrimination capacity, which we model here by means of similarity relations. We assume that each agent builds procedural preferences de ned on the space of expected payoffs-strategy frequencies attached to his current strategy. These preferences, together with an adaptive learning process lead to doubt-based selection dynamic systems. We introduce the concepts of Mixed Strategy Doubt Equilibria, Mixed Strategy Doubt-Full Equilibria and Mixed Strategy Doubtless Equilibria and show the theoretical and the empirical relevance of these concepts.

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Paper provided by Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I in its series IKERLANAK with number 2008-31.

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Date of creation: Dec 2007
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Handle: RePEc:ehu:ikerla:200831

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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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  1. Ignacio Palacios-Huerta & Oscar Volij, . "Experientia Docet: Professionals Play Minimax In Laboratory Experiments," Economic theory and game theory 019, Oscar Volij.
  2. 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.
  3. Antonio Cabrales, 1993. "Stochastic replicator dynamics," Economics Working Papers 54, Department of Economics and Business, Universitat Pompeu Fabra.
  4. 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.
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  8. Karl H. Schlag, 1995. "Why Imitate, and if so, How? A Bounded Rational Approach to Multi-Armed Bandits," Discussion Paper Serie B 361, University of Bonn, Germany, revised Mar 1996.
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  13. 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.
  14. Tang, Fang-Fang, 2001. "Anticipatory learning in two-person games: some experimental results," Journal of Economic Behavior & Organization, Elsevier, vol. 44(2), pages 221-232, February.
  15. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
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  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. Sushil Bikhchandani & David Hirshleifer & Ivo Welch, 1998. "Learning from the Behavior of Others: Conformity, Fads, and Informational Cascades," Journal of Economic Perspectives, American Economic Association, vol. 12(3), pages 151-170, Summer.
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