Optimal mechanism for the sale of a durable good

Résumé

We show that posted prices are the optimal mechanism to sell a durable good to a privately informed buyer when the seller has limited commitment in an infinite horizon setting. We provide a methodology for mechanism design with limited commitment and transferable utility. Whereas in the case of commitment, subject to the buyer’s truthtelling and participation constraints, the seller’s problem is a decision problem, in the case of limited commitment, the seller’s problem corresponds to an intrapersonal game, where different “incarnations” of the seller represent the different beliefs he may have about the buyer’s valuation.