The Optimality of Being Efficient: Designing Auctions

Abstract

A cornerstone of the auction literature is the theory of"optimal auctions."'This theory uses mechanism design techniques to characterize, in general settings, the auction that maximizes the seller's expected revenues. One feature of the solution is that typically there is a conflict between the goals of revenue maximization and efficiency. The revenue-optimizing seller often either places goods in hands other than those who value them the most or withholds goods entirely from the market. However, the conclusion that the seller gains by assigning goods inefficiently depends critically on two strong assumptions: (1) the seller can prevent resale among bidders from occurring after the auction; and (2) the seller can commit to not sell the withheld goods after the auction. In this paper, the authors examine how the optimal auction problem changes when one or both of these assumptions are relaxed. This paper is organized as follows. In section 2, the authors establish the seller's general incentive to misassign goods and they identify settings where the optimal auction is efficient. In section 3, they solve two variations on the optimal auction, which recognize the possibility of resale. Section 4 proves that perfect resale destroys the seller's incentive to misassign goods. Section 5 establishes that with perfect resale, any misassignment of goods results in strictly lower seller revenues than the best efficient assignment. In section 6, the paper shows that the Vickrey auction is not distorted by the possibility of resale.

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