Optimal auctions with sequential arrival: Allowing for re-auction and resale

The sequential arrival of bidders is a crucial aspect of real-world auctions, providing the auctioneer with incentives for re-auctioning and bidders with opportunities for resale. This paper investigates the optimality of sequential auctions, focusing on scenarios where the auctioneer can re-auction items and tap into potential future resale demand. Specifically, when bidders arrive in two batches, the auctioneer first conducts an English auction for the initial batch. If unsuccessful, the item is re-auctioned to both batches of bidders; otherwise, the winner can opt to resell to current and future bidders. I characterize the optimal sequential English auctions, noting that the auctioneer's belief about the value distribution of the first batch is necessarily limited after the initial auction fails. The findings demonstrate that, on the optimal reserve price path, the first batch always retains a positive winning probability in the re-auction. Furthermore, I identify conditions under which resale does not occur in equilibrium due to a high optimal reserve price in the initial auction. Thus, when the auctioneer can set optimal reserve prices and access resale demand, resale can be implicitly prohibited. These results provide important policy implications for auctions in both the private and public sectors.