How To Sell (or Procure) in a Sequential Auction

TL;DR

This paper characterizes the optimal selling mechanism in a sequential auction setting with one seller and multiple buyers, introducing new techniques to handle the failure of the first-order approach and showing how to significantly increase revenue.

Contribution

It develops a novel method for designing optimal mechanisms in sequential auctions where traditional approaches fail, including specific transfer and withholding rules.

Findings

Optimal mechanism involves transfers to top two bidders and allocation to second-highest bidder.

Withholding rules depend on top valuations and can be implemented via modified third-price or pay-your-bid auctions.

The proposed mechanism significantly outperforms standard reserve prices in revenue generation.

Abstract

A seller with one unit of a good faces N\geq3 buyers and a single competitor who sells one other identical unit in a second-price auction with a reserve price. Buyers who do not get the seller's good will compete in the competitor's subsequent auction. We characterize the optimal mechanism for the seller in this setting. The first-order approach typically fails, so we develop new techniques. The optimal mechanism features transfers from buyers with the two highest valuations, allocation to the buyer with the second-highest valuation, and a withholding rule that depends on the highest two or three valuations. It can be implemented by a modified third-price auction or a pay-your-bid auction with a rebate. This optimal withholding rule raises significantly more revenue than would a standard reserve price. Our analysis also applies to procurement auctions. Our results have implications for sequential competition in mechanisms.