Auctions vs. Negotiations: Optimal Selling Mechanism with Endogenous Bidder Values

Abstract

This paper studies the design of the revenue maximizing selling mechanism in a scenario where bidders can make costly investments upfront to enhance their valuations. Unlike the case where bidders' values are exogenously fixed, here it may be profitable for the seller to discriminate among ex ante symmetric bidders. I first identify a sufficient and almost necessary condition under which symmetric auctions are optimal. When this condition fails, the optimal selling mechanism may be discriminatory. I further find that the optimal mechanism in general follows a structure which I call a threshold mechanism. Two extreme examples of the threshold mechanism are symmetric auctions and sequential negotiations. In general, any threshold mechanism can be implemented by a dynamic selling scheme which alternately utilizes auctions and negotiations.