Commitment, Trembling Hand Imperfection and Observability in Games

Abstract

In an important contribution Bagwell [1995] showed that the value of commitment tends to vanish if the observability of commitments is subject to an arbitrarily small distortion, due to the possibility of misunderstanding or communication error. Bagwell's observation calls into question the many stage games that have been exceedingly popular in economics, especially in theoretical industrial organization. The present paper contributes to assess the robustness of Bagwell's result. We add other distortions to Bagwell model, such as in players' execution of actions. We show that the unique pure strategy equilibrium of the game converges to the unique equilibrium outcome of the simultaneous move game with perfect observability if the noise associated with the observation of the leader's choice is small relative to the probability of trembles or if there are many other such imperfections. These results suggest that Bagwell's result is driven by his exclusive consideration of a particular distortion, and is not robust in the face of additional plausible distortions.