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 finitetype 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.