Which to Sell First? Optimal Ordering of Heterogeneous Items in Sequential Auctions
46 Pages Posted: 24 Jan 2017 Last revised: 27 Nov 2017
Date Written: November 21, 2017
We study the optimal ordering of heterogeneous items in first-price and second-price (sealed-bid) 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). When items are vertically differentiated, i.e. valuations of all items increase with buyers’ types, ordering the items in decreasing level of quality is the unique order to achieve full efficiency, if valuations exhibit strict increasing differences (SID) in item quality and buyer type. If in addition (SID) holds for item quality and buyers virtual values, sequential auctions with the previously-mentioned order achieve the optimal revenue among all mechanisms that are Bayesian incentive compatible, individually rational, and sell- ing all items. When items are horizontally differentiated, i.e. valuations of (the two) items move in opposite directions with buyers types, ordering does not matter: either order 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 items.
Keywords: Sequential auctions, Mechanism design, Ordering, Efficiency, Optimality, Vertical differentiation, Horizontal differentiation
JEL Classification: D44, D82
Suggested Citation: Suggested Citation