Dynamic contracting under positive commitment

Abstract

We consider a firm that sells products that arrive over time to a buyer. We study this problem under a notion we call positive commitment, where the seller is allowed to make binding positive promises to the buyer about items arriving in the future, but is not allowed to commit not to make further offers to the buyer in the future. We model this problem as a dynamic game where the seller chooses a mechanism at each period subject to a sequential rationality constraint, and characterize the perfect Bayesian equilibrium of this dynamic game. We prove the equilibrium is efficient and that the seller's revenue is a function of the buyer's ex ante utility under a no commitment model. In particular, all goods are sold in advance to the buyer at what we call the positive commitment price.