Economic Theory Seminar Series: Robustly Optimal Auctions with Unknown Resale Opportunities

Gabriel Carroll | Stanford

The standard revenue-maximizing auction discriminates against a priori stronger bidders so as to reduce their information rents.  We show that such discrimination is no longer optimal when the auction's winner may resell to another bidder, and the auctioneer has non-Bayesian uncertainty about such resale opportunities (including possible leakage of private information before resale).  We consider a "worst-case" resale procedure in which the highest-value bidder learns all bidders' values and has full bargaining power.  With this form of resale, misallocation no longer reduces the information rents of the high-value bidder, as he could still secure the same rents by buying the object in resale.  When the auctioneer must sell the object, the simple second-price auction proves to be optimal.  If the auctioneer may withhold the object, then under regularity assumptions, we show that revenue is maximized by a "Vickrey auction with bidder-specific reserve prices" first proposed by Ausubel and Cramton (2004).  The proof of optimality involves constructing Lagrange multipliers on a double continuum of binding non-local incentive constraints.