Optimal Selling Mechanisms under Imperfect Commitment

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