Optimal Ordering in Sequential Auctions

Abstract

We study the optimal ordering of first-price and second-price (sealed-bid) sequential auctions with multiple items and unit-demand buyers. When items are vertically differentiated and buyers' valuations exhibit strict increasing differences (SID) in item quality and buyer type, ordering the items in decreasing level of quality achieves full efficiency. If (SID) also holds for buyers' virtual values, the same ordering achieves the optimal revenue among all mechanisms that are Bayesian incentive compatible, individually rational, and selling all items. When items are horizontally differentiated, we show that the ordering does not matter: either ordering gives a fully efficient outcome and the same revenue for the seller. Our analysis on efficient ordering generalizes to the mixed case where items can be divided into two groups such that there is vertical differentiation within each group, and horizontal differentiation across groups. In this setup, it is optimal to order items in decreasing level of quality within each group, and that it does not matter how items belonging to the two different groups are assorted. Our analysis provides partial justification for employing sequential auctions in the sale of multiple similar items.

Keywords: Sequential auctions, Mechanism design, Ordering, Efficiency, Optimality, Vertical differentiation, Horizontal differentiation

JEL Classification: D44, D82