Implementing Optimal Outcome through Sequential Auctions

Abstract

We study the optimal design of sequential auctions to sell heterogeneous items to buyers with private values and unit demand. The valuation of each item depends on a buyer’s private type and item-specific characteristics. We show that a sequence of arbitrary standard auctions, ordered in decreasing variation of buyers’ valuations, achieves full efficiency and constrained optimal revenue subject to (BIC), (IIR) and an all-sold condition. In addition, any sequential l-th price auction with the same ordering and optimal static reserve prices achieves optimal revenue subject to (BIC) and (IIR). We also provide discussions with respect to bid revelation policies and seller’s commitment power. Our analysis shows that in contrast to simultaneous auctions, a properly de- signed sequential auction is an indirect optimal selling procedure in the current setting, providing justification for its wide real-life applications.

Keywords: Optimal mechanism; Sequential auction; Standard auction; Bid disclosure

JEL Classification: D44, D82