Nonlinear Pricing with Asymmetric Competition and Complete Information

Our model is a three-stage game with complete information in which a dominant firm offers a general tariff first and then a rival firm responds with a per-unit price, followed by a buyer making her decision to purchase from one or both firms. We characterize SPE of the game and study the implications of the equilibrium outcome. Our paper makes three main contributions. First, it provides a novel explanation for the prevalence of nonlinear pricing under duopoly in the absence of private information: The dominant firm can use a menu of offers to constrain its rival's choices and extract surplus from the buyer. Second, it shows that when the capacity of the rival firm is constrained, as compared to linear pricing schemes, the nonlinear pricing tariff adopted by the dominant firm reduces the price, sales, and profits of the rival firm as well as the buyer's surplus. Third, we establish an equivalence between a subgame perfect equilibrium of the game and an optimal mechanism in a “virtual” principal-agent model with hidden action and hidden information. As a result of such an equivalence, we can apply mechanism design techniques to solve for SPE of the game.