Mergers in Sealed vs. Oral Asymmetric Auctions

In this paper, we study mergers in sealed-bid asymmetric auctions. By asymmetric, we mean that bidders are drawing values out of extreme value distributions with di erent means. We develop an algorithm to nd numerical solutions of the system of di erential equations for the inverse bidding functions at equilibrium. The equilibrium inverse bidding functions are found to have a singularity, a critical value above which no bids are made, regardless of a bidder's value. It is shown that the e ects of symmetry-decreasing mergers are smaller in sealed-bid auctions than in oral auctions, and vice-versa. Not only are the symmetry-decreasing merger e ects smaller in sealed-bid auctions, but the marginal cost reduction necessary to o set a given price e ect is also smaller. Despite the di erence between sealed and oral auctions, sealed-bid merger e ects are closely approximated by an Her ndahllike formula derived from moment restrictions in oral auctions. The source of this curious similarity is not apparent.