Optimal Mechanism for the sale of a durable good
with Vasiliki Skreta
We characterize the revenue-maximizing Perfect Bayesian equilibrium for a seller who owns one unit of a durable good and interacts with a privately informed buyer over infinitely many periods. In each period, the seller can design a mechanism that determines the rules of trade. In the revenue-maximizing equilibrium, as long as a sale has not occurred, the seller chooses a mechanism that can be implemented as a posted price. Conceptually, this shows that the shape of the revenue-maximizing mechanism to sell a durable good is the same under commitment or limited commitment. Methodologically, the paper provides a recipe for problems of mechanism design with limited commitment. While in the case of commitment, subject to the truthtelling and participation constraints of the buyer, the seller's problem is a decision problem, in the case of limited commitment, we show that the seller's problem can be represented as an intrapersonal equilibrium, where the different “incarnations" of the seller represent the different beliefs he may have about the buyer's valuation.
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