We consider private value auctions where bidders’ types are dependent, a case usually
treated by assuming affiliation. We show that affiliation is a restrictive assumption in
three senses: topological, measure-theoretic and statistical (affiliation is a very
restrictive characterization of positive dependence). We also show that affiliation’s
main implications do not generalize for alternative definitions of positive dependence.
From this, we propose new approaches to the problems of pure strategy equilibrium
existence in first-price auctions (PSEE) and the characterization of the revenue ranking
of auctions. For equilibrium existence, we slightly restrict the set of distributions
considered, without loss of economic generality, and offer a complete characterization
of PSEE. For revenue ranking, we obtain a characterization of the expected revenue
differences between second and first price auctions with general dependence of types