Optimal auction design under non-commitment

We characterize revenue-maximizing mechanisms in Myerson's (1981) environment when the seller behaves sequentially rationally, in the sense that she cannot commit not to propose a new mechanism if the previously chosen one fails to allocate the object. We show that the seller-optimal mechanism takes the same form as in the case when there is commitment: The seller maximizes revenue by assigning, at t=1t=1, the good to the buyer with the highest virtual valuation if it is above a buyer-specific reserve price. If no trade takes place at t=1t=1, at t=2t=2, the seller assigns the object to the buyer with the highest posterior virtual valuation, provided that it is above the seller's value.