Optimal Ordering in Sequential Auctions with One-Dimensional Types

Abstract

We study the optimal ordering of first-price and second-price (sealed-bid) sequential auctions with one-dimensional types. In the case of positive one-dimensional association, we show a welfare-maximizing seller always want to order items in ‘decreasing spread’ when such ordering exists and the outcome is fully efficient. If the valuations of items admit a stronger ordering of ‘strong decreasing spread’, we show a profit-maximizing seller prefers the same ordering and constrained optimal revenue is achieved. We also consider generalizations to negative and mixed one-dimensional association. In the negative case, we show ordering does not matter, and either one gives a fully efficient outcome, though seller’s revenue is no longer constrained optimal. For efficiency alone, intuitions from the positive and negative cases apply to mixed one-dimensional association: Within either group, it is optimal to order items in ‘decreasing spread’ when such ordering exists, while the ordering across the two groups does not matter. Our analysis provides a partial explanation for the prevalence of sequential auctions.