Optimal Nonlinear Pricing by a Dominant Firm under Competition

We consider a nonlinear pricing problem faced by a dominant firm competing with a minor firm. The dominant firm offers a general tariff first and then the minor firm responds with a per- unit price, followed by a buyer choosing her purchases. By developing a "mechanism design approach" to solve the subgame perfect equilibrium, we characterize the dominant firm's optimal nonlinear tariff, which exhibits convexity and yet can display quantity discounts. In equilibrium the dominant firm uses a continuum of unchosen offers to constrain its rival's potential deviations and extract more surplus from the buyer. Antitrust implications are also discussed.