CASOS Working PAPER

"Uncommon Knowledge: Behavior and Learning in the "Dirty Faces" Game" (PDF file)
Author: Roberto A. Weber

Abstract
This paper presents and examines, as a Bayesian game, the Dirty Faces problem discussed by Littlewood (1953). The equilibrium prediction of behavior in this game makes extreme assumptions on the rationality of the players and on their beliefs concerning the rationality of others. Common knowledge of rationality among the players is required for the solution to arise in the general form of the game. The exact number of steps of iterated rationality necessary for equilibrium to arise, however, depends on the number of players of a particular type.
An experiment is used to test the actual behavior of subjects. While behavior at the group level is inconsistent with the game-theoretic prediction, individual level behavior shows a greater degree of consistency with theory. Three models that incorporate error into players' actions all do better than the standard theory in predicting behavior. Finally, a second set of experiments find support for the hypothesis that learning occurs with experience.