The Dirty Faces Game Revisited

Weber (2001) uses the Dirty Faces Game to examine the depth of iterated rationality. Weber does not consider equilibria that contain weakly dominated actions. So he implicitly assumes that it is common knowledge that no one ever uses weakly dominated actions. We show that allowing for equilibria in weakly dominated strategies greatly extents the set of potentially rational actions. The original game therefore lacks discriminatory power, as many actions categorised as irrational by Weber can actually be part of an equilibrium strategy. We slightly modify the payoff structure and establish strict dominance, which leads to a unique equilibrium. The resulting dominance-solvable game is implemented in an experiment. We find that subjects are either able to iterate right to the equilibrium or fail to do so when two or more steps of iteration are necessary. Virtually all subjects were able to do one step of iteration. Further, we find evidence that the lack of confidence in other players' iterative abilities induces deviations from equilibrium play.