“Nonlinear Pricing with Asymmetric Competition” by Prof. Tan Guofu
University of Southern California
University of Louisville
Adam Chi Leung Wong
Shanghai University of Finance and Economics
Motivated by several recent antitrust cases, we study a strategic model of competition in intermediate-goods markets. 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 subgame perfect equilibria of the game and study the implications of the equilibrium outcome.
Our paper makes three major contributions. First, it provides a novel explanation for the prevailence of nonlinear pricing (a menu of offers conditional on volumes) under oligopoly 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. In other words, nonlinear pricing may have antitrust implications in the sense that it can lead to partial foreclosure and harm consumer welfare. 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. This involves treating the rival firm's (an agent's) price as its hidden action meanwhile letting the buyer (another agent) to report the rival firm's price as her private information to the dominant firm (the principal). As a result of such an equivalence, we can apply mechanism design techniques to solve for subgame perfect equilibria of the game.