Bidding into the Red: A Model of Post-Auction Bankruptcy

This paper investigates auctions where bidders have limited liability. First, we analyze bidding behavior under different auction formats, showing that the second-price auc-tion induces higher prices, higher bankruptcy rates, and lower utilities than the first-price auction. Second, we show that the cost of bankruptcy critically affects the seller’s preference over the choice of auction. If bankruptcy is very costly, the seller prefers the first-price auction over the second-price auction. Alternatively, if the bankrupt assets are resold among the losers of the initial auction, the seller prefers the second-price auction. AUCTIONS ARE BECOMING AN EVER MORE POPULAR way to allocate important, large-scale property rights. A major concern in such large auctions is that agents may bid aggressively, anticipating that they can declare bankruptcy if the good is worth less than expected. This problem is frequently encountered when selling large assets. For example, ITV Digital went bankrupt after aggressively bid-ding for the right to broadcast Football League games, owing £178m. Default is also common in procurement auctions. For example, Connex’s rail franchise for southeast England was taken over by the government after it demanded ex-tra subsidies to continue operating. These examples illustrate the prevalence of post-auction bankruptcy and provide a cautionary tale: As auction mecha-nisms become an increasingly useful tool for both government and industry, the possibility of default should be taken into account when designing the auction. The basic structure of the paper follows the seminal work of Waehrer (1995), Rhodes-Kropf and Viswanathan (2000), and Zheng (2001). The seller first auc-tions a good among a number of bidders. After the auction, uncertainty is revealed and the winning bidder decides whether to declare bankruptcy or pay his bid.1 The contribution of this paper is twofold. First, we analyze the effect of differ-ent auction formats on bidding behavior. We find that the second-price auction (SPA) induces higher prices, higher bankruptcy rates, and lower utilities than the first-price auction (FPA). This analysis is important because the choice o