Optimal Auction Design Under Non-Commitment

Abstract

This paper characterizes revenue maximizing auctions for a Önite horizon version of the standard IV P model of Myerson (1981) for a seller who cannot commit not to propose a new mechanism, if previously chosen ones fail to allocate the object. We show that a revenue maximizing mechanism in the Örst period assigns the good to the buyer with the highest virtual valuation, provided that it is above a buyer-speciÖc reserve price. If no buyer obtains the good in the Örst period, the same procedure is repeated in the second period, where virtual valuations are calculated using the posterior distributions and the reserves prices are lower, and so forth, until we reach the last period of the game. This is the Örst paper that characterizes optimal mechanisms in a multi-agent environment where the designer behaves sequentially rationally.