A Common-Value Auction With State-Dependent Participation

This paper analyzes a common-value, First-price auction with state-dependent participation. The number of bidders, which is unobservable to them, depends on the true value. For exogenously given participation patterns that involve many bidders in each state, the bidding equilibrium may be of a pooling type with high probability, the winning bid is the same across states and is below the ex-ante expected value or of a partially revealing type with no significant atoms in the winning bid distribu- tion and an expected winning bid increasing in the true value. Which of these forms will arise is determined by the likelihood ratio at the top of the signal distribution and the participation across states. When the state-dependent participation is endogenized as the strategic solicitation by an informed seller who bears a small cost for each solicited bidder, an equilibrium of the partially revealing type always exists and is unique of this type; for certain signal distributions there also exist equilibria of the pooling type.