Affiliation, equilibrium existence and revenue ranking of auctions

Affiliation has been a prominent assumption in the study of economic models with statistical dependence. Despite its large number of applications, especially in auction theory, affiliation has limitations that are important to be aware of. This paper shows that affiliation is a restrictive condition and the intuition usually given for its adoption may be misleading. Also, other usual justifications for affiliation are not compelling. Moreover, some implications of affiliation - namely, equilibrium existence in first-price auctions and the revenue dominance of second-price auctions - do not generalize to other definitions of positive dependence.