Games with imperfectly observable commitment

K. Bagwell (1995, Games Econ. Behav. 8, 271-280) claims that, in models of commitment, ''the first-mover advantage is eliminated when there is a slight amount of noise associated with the observation of the first-mover's selection.'' We show that the validity of this claim depends crucially on the restriction to pure strategy equilibria. The game analyzed by Bagwell always has a mixed equilibrium that is close to the Stackelberg equilibrium when the noise is small. Furthermore, an equilibrium selection theory that combines elements from the theory of Harsanyi and Selten (1988, A General Theory of Equilibrium Selection in Games. Cambridge, MA: MIT Press) with elements from the theory of Harsanyi (1995, Games Econ. Behav. 8, 91-122), actually selects this ''noisy Stackelberg equilibrium.'' (C) 1997 Academic Press.