Dynamic Contracting under Positive Commitment

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.

A Theory of Credibility under Commitment

The ability to commit to a contract may increase a player's payoff. In a repeated relationship, the lack of a complete contingency contract is usually explained by the presence of contracting costs. We study optimal contracts in a specific class of credibility models: relationships in which the surplus comes solely from screening. We show that the optimal contract is to reproduce the Perfect Bayesian Equilibrium of the game without commitment. In this sense, sequential rationality constraints do not bind. Therefore, we provide an alternative explanation for why a specific class of long-term relationships may often not be contracted upon.