How to sell to buyers with crossholdings

Abstract

This paper characterizes the optimal selling mechanism in the presence of horizontal crossholdings. We find that this mechanism imposes a discrimination policy against the stronger bidders so that the seller´s expected revenue is increasing in both the common crossholding and the degree of asymmetry in crossholdings. Furthermore, it can be implemented by a sequential procedure that includes a price-preferences scheme and the possibility of an exclusive deal with the weakest bidder. We also show that a simple sequential negotiation mechanism, although suboptimal, yields a larger seller´s expected revenue than both the first-price and the second-price auctions.