Optimal selling mechanisms under imperfect commitment

This paper studies the optimal mechanisms for a seller with imperfect commitment who puts up for sale one individual unit per period to a single buyer in a dynamic game. The buyer's willingness to pay remains constant over time and is his private information. In this setting, the seller cannot achieve greater payoffs than those obtained by posting a price in each period. However, price posting is not optimal if the buyer is sufficiently impatient relative to the seller. It is also proved that a mechanism à la Goethe (see Moldovanu and Tieztel 1998) is almost optimal.