Competitive bidding and proprietary information

We consider the sale of an object by sealed-bid auction, when one bidder has private information and the others have access only to public information. The equilibria of the bidding game are determined, and it is shown that at equilibrium the informed bidder's distribution of bids is the same as the distribution of the maximum of the others' bids. The expected profit of the informed bidder is generally positive, while the other bidders have zero expected profits. The equilibrium bid distributions and the bidders' expected profits are shown to vary continuously in the parameters of the bidding game.