Sequentially Optimal Mechanisms

We characterize the revenue maximizing mechanism in a two-period model. A risk neutral seller owns one unit of a durable good and faces a risk neutral buyer whose valuation is private information. The seller has all the bargaining power; she designs an institution to sell the object at t=0 but she cannot commit not to change the institution at t=1 if trade does not occur at t=0. The seller’s objective is to pick the revenue maximizing mechanism. We show that if the probability density function of the buyer’s valuation satisfies certain conditions, the optimal mechanism is to post a price in each period. Previous work has examined price dynamics when the seller behaves sequentially rationally. We provide a reason for the seller’s choice to post a price even though she can use infinitely many other possible institutions: posted price selling is the optimal strategy in the sense that it maximizes the seller’s revenues.