First?price auctions when the ranking of valuations is common knowledge

Abstract

We consider a first–price auction when the ranking of bidders' private valuations is common knowledge among bidders. This new informational framework is motivated by several applications, from procurement to privatization. It induces a particular asymmetric auction model with affiliated private values that has several interesting properties but raises serious technical complications. We prove existence and uniqueness of equilibrium in pure strategies and show that the seller's reven generally higher in a first–price than in second–price and English auctions, in contrast to the ranking in the affiliated values model by Milgrom and Weber. This also implies that in first–price auctions, providing information concerning the ranking of valuations among bidders tends to increase the seller's expected revenue.