Sequential Auctions with Information About Future Goods

When capacity-constrained bidders have information about a good sold in a future auction, they need to take the information into account in forming today's bids. The capacity constraint makes even otherwise unrelated objects substitutes and creates an equilibrium link between future competition and current bidding strategy. This paper proves the existence and uniqueness of a symmetric pure-strategy equilibrium under mild conditions on the population distribution of valuations, characterizes general properties of the equilibrium bidding strategy, and provides a simple technique for numerically approximating the bidding strategy for arbitrary valuation distributions. The key property of the equilibrium is that almost all bidders submit positive bids in the first stage, thereby ensuring trade with probability one. Even bidders who strongly prefer the second object submit a positive bid in the first auction, because losing the first auction is informative about the remaining competitors who also lost, and losing with a low bid indicates that these competitors are quite strong. Because of the guaranteed trade, the sequential auction with information about future goods is a very efficient trading mechanism, achieving more than 98 percent of the potential gains from trade across a wide variety of settings.