Reserve price signaling in first-price auctions with an uncertain number of bidders

摘要

We study first-price auctions in which the number of bidders is the seller's private information, and investigate the use of a reserve price to signal this private information. We use the D1 criterion to refine the set of equilibria and characterize a symmetric separating equilibrium outcome, where the reserve price increases with the number of bidders. The key driving force is a certain form of single-crossing property. With more bidders, the seller can afford a high reserve price that discourages competition in the auction, for the winning bid is more likely to be higher.