Games with Imperfectly Observable Commitment

Eric van Damme and Sjaak Hurkens

Abstract: In Bagwell (1995) it is claimed 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) with elements from the theory of Harsanyi (1995), actually selects this `noisy Stackelberg equilibrium.'

Keywords: Commitment, equilibrium selection.

Classification Number: C72.

Games and Economic Behavior 21:282-308 (1997)