Endogenous entry in auctions with negative externalities

In this paper, we study the auction to allocate an indivisible good when each potential buyer has a private and independent valuation for the item and suffers a negative externality if a competitor acquires it. In that case, the outside option of each buyer is mechanism-dependent, which implies that participation is endogenous. As several works in the literature have shown, the optimal auction entails strong threats to induce full entry and maximal expected revenue. This results from the full commitment assumption, which ensures that threats are credible. We show that absent credible threats, the entry process does not lead to full participation: the equilibrium entails screening of agents in the entry stage and a trade-off between reserve prices and entry fees. Besides, we discuss the conditions under which the impossibility to use threats does not prevent the seller from ensuring a minimal screening and reaching a high expected revenue.