A Common Value Auction with Bid Solicitation

Abstract

We study a first-price auction for a single good with common values. The novel feature is that the number of bidders is endogenous: the seller (auctioneer) knows the value and solicits bidders. Soliciting bidders is costly. The bidders privately observe noisy signals of the true value, as in the standard auction model. However, the number of solicited bidders is unobservable to them. The number of bidders that the seller solicits depends on the true value, giving rise to a solicitation effect: Being solicited conveys information. The solicitation effect is a key difference to standard common value auctions. In contrast to standard auctions, bidders may pool on a common price, giving rise to atoms. We discuss information aggregation in the case of small bidder solicitation cost. We show that there is a type of equilibrium that aggregates information well when the most favorable signals are informative. However, there is also an equilibrium that fails to aggregate information.