Implementing Optimal Mechanisms through Sequential Auctions

Abstract

We study the optimal ordering of heterogeneous items in sequential auctions with unit-demand buyers. The valuation of each item depends on a buyer’s private type and an item-specific characteristic (e.g. quality). We assume “generalized vertical differentiation”, i.e. valuations of all items increase in buyers’ types. In this setting, it is optimal to sell items in decreasing level of quality: it achieves full efficiency if valuations exhibit strict increasing differences (SID) in item quality and buyers’ types. In addition, when reserve prices are allowed, sequential auctions with the above-mentioned order and optimal single-item reserve prices maximize the seller’s revenue among all mechanisms that satisfy (BIC) and (IIR). We show both efficiency and revenue-maximization are robust to auction formats, such as sequential first-price, second-price, and English auctions. Our analysis shows that a properly ordered sequential auction is an optimal indirect selling mechanism, providing justification for its wide real-life applications.

Keywords: Sequential auction; Mechanism design; Ordering; Optimality; Vertical differentiation; Reserve price

JEL Classification: D44, D82