Optimal mechanism for the sale of a durable good
A buyer wishes to purchase a durable good from a seller who in each period chooses a mechanism under limited commitment. The buyer's valuation is binary and fully persistent. We show that posted prices implement all equilibrium outcomes of an infinite-horizon, mechanism selection game. Despite being able to choose mechanisms, the seller can do no better and no worse than if he chose prices in each period, so that he is subject to Coase's conjecture. Our analysis marries insights from information and mechanism design with those from the literature on durable goods. We do so by relying on the revelation principle in Doval and Skreta (2020).