On Competitive Nonlinear Pricing∗

A buyer of a divisible good faces several identical sellers. The buyer’s preferences are her private information, and they may directly affect the sellers ’ profits (common values). Sellers compete by posting menus of nonexclusive contracts, so that the buyer can simultaneously and privately trade with several sellers. We focus on the finite-type case, and we provide a full characterization of pure-strategy equilibria in which sellers post convex tariffs. All equilibria involve linear pricing. When the sellers ’ cost functions are linear and do not depend on the buyer’s type (private values), equilibria exist and trade is efficient. Under common values, or when the sellers ’ costs are strictly convex, there is a severe form of market breakdown as at most one type of the buyer may actively trade. Moreover equilibria exist only under restrictive conditions