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Behavior and Learning in the “Dirty Faces” Game

Published online by Cambridge University Press:  14 March 2025

Roberto A. Weber
Roberto A. Weber*
Affiliation:
Department of Social and Decision Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA
*
email: rweber@andrew.cmu.edu
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Abstract

This paper examines the Dirty Faces problem as a Bayesian game. The equilibrium in the general form of the game requires the extreme assumption of common knowledge of rationality. However, for any finite number of players, the exact number of steps of iterated rationality necessary for the equilibrium to arise depends on the number of players of a particular type, allowing the game to be used to bound the number of steps satisfied by actual players. The game differs from other games used to study iterated rationality in that all players are better off when common knowledge of rationality is satisfied. While behavior in experiments is inconsistent with the game-theoretic prediction at the group level, individual level behavior shows a greater degree of consistency with theory and with previous results on iterated rationality. Finally, there is some evidence of learning in repeated play.

Keywords

game theorycommon knowledge

JEL classification

C91: Laboratory, Individual BehaviorC92: Laboratory, Group BehaviorC72: Noncooperative Games

Information

Type
Research Article
Information
Experimental Economics , Volume 4 , Issue 3 , December 2001, pp. 229 - 242
Copyright
Copyright © 2002 Economic Science Association

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