On Auctions with Withdrawable Winning Bids

This paper considers sealed bidding in which bidders may submit two or more bids and after the bids are opened may, perhaps at a cost, withdraw bids that are more aggressive than would be necessary to win. Such withdrawal strategies are sometimes followed, but currently are surreptitious. However, legitimization of them would create potentially useful market mechanisms of potential interest to government agencies. These market mechanisms are also of theoretical interest since they are intermediate between first-price and second-price auctions. This paper presents models of such auctions. Both decision-theoretic models (applicable to surreptitious use of withdrawal strategies) and game theoretic models appropriate for openly withdrawable bid situations are developed. We describe a particular auction in which a winning bid was withdrawn and fit one of our decision theoretic models to data from it.