Selling to Intermediaries: Optimal Auction Design in a Common Value Model

We characterize revenue maximizing auctions when the bidders are intermediaries who wish to resell the good. The bidders have differential information about their common resale opportunities: each bidder privately observes an independent draw of a resale opportunity, and the highest signal is a sufficient statistic for the value of winning the good. If the good must be sold, then the optimal mechanism is simply a posted price at which all bidders are willing to purchase the good, and all bidders are equally likely to be allocated the good, irrespective of their signals. If the seller can keep the good, then under the optimal mechanism, all bidders make the same expected payment and have the same expected probability of receiving the good, independent of the signal. Conditional on the good being sold, the allocation discriminates in favor of bidders with lower signals. In some cases, the optimal mechanism again reduces to a posted price. The model provides a foundation for posted prices in multi-agent screening problems.