Asymmetric Auctions with Endogenous Participation

We study endogenous participation in asymmetric second price auctions where one bidder is "special". We show seller revenue decreases whenever the special bidder becomes more dominant in the sense of FOSD, or more generally whenever the other bidders' profits are reduced. We also establish an equivalence result for second price auctions - any arbitrary distribution of the special bidder's value is "competitively equivalent" to one that is a power function of the value distribution of the other bidders. Finally, we analyze first-price auctions numerically and show that our results extend to this alternate mechanism.