The Department of Economics at the University of Warwick presents the full text of the research paper entitled "Three Principles of Competitive Nonlinear Pricing," by Frank H. Page, Jr. and Paulo K. Monteiro that was published in May 2001. The paper is in PDF format. The authors discuss nonlinear pricing games and Nash equilibrium, the competitive taxation principle, the delegation principle, and the competitive revelation principle.
"Many businesses focus on driving volume or reducing costs rather than increasing price under the mistaken belief they have greater control over volume and costs than price. Yet, a 1% increase in price (holding volume fixed) has a greater impact on operating profit than a 1% increase in volume or a 1% decrease in cost. By not seizing the initiative on price, businesses abrogate decisions about price to competitors, customers, and the channel. A careful analysis and understanding of those same actors could help them price in a more profitable manner. Hence, this book, which is designed to communicate the fundamental principles of pricing. In marked contrast to other books on pricing, this one is based on economic theory. This is not to deny the value to be had from looking at pricing through other lenses. It is simply that these other lenses do not yet provide a systematic and organized way to think about pricing. Economic theory does. Its power is not in the provision of to-do lists or the Gradgrind-like accumulation of facts.8 Rather, it is in generating the right questions to be asked. Both our own experiences and that related to us by our students who have taken our classes has confirmed us in this view. A second point of contrast with other treatments of pricing is that we convey principles through stylized examples rather than anecdotes"--Provided by publisher.
What do phone rates, frequent flyer programs, and railroad tariffs all have in common? They are all examples of nonlinear pricing. Pricing is nonlinear when it is not strictly proportional to the quantity purchased. The Electric Power Research Institute has commissioned Robert Wilson to review the various facets of nonlinear pricing. The work starts with a general non-mathematical discussion, followed by a more technical presentation intended for readers with a fairly advanced background. Thorough and detailed, this study has ample examples of case studies from a variety of industries.
We consider a nonlinear pricing problem faced by a dominant firm which competes with a capacity-constrained minor firm for a downstream buyer who may purchase the product from the firms under complete information. Specifically, we analyze a three-stage game in which the dominant firm offers a general tariff first and then the minor firm responds with a per-unit price, followed by the buyer choosing her purchases. By establishing an equivalence between the subgame perfect equilibrium of our asymmetric competition game and the optimal mechanism in a “virtual” principal-agent model, we characterize the dominant firm's optimal nonlinear tariff, which exhibits convexity and yet can display quantity discounts. Our analysis provides a rationale for nonlinear pricing under competition in the absence of private information: The dominant firm can use unchosen offers to constrain its rival's possible deviations and extract more surplus from the buyer. Antitrust implications are also discussed.
The first volume of this wide-ranging Handbook contains original contributions by world-class specialists. It provides up-to-date surveys of the main game-theoretic tools commonly used to model industrial organization topics. The Handbook covers numerous subjects in detail including, among others, the tools of lattice programming, supermodular and aggregative games, monopolistic competition, horizontal and vertically differentiated good models, dynamic and Stackelberg games, entry games, evolutionary games with adaptive players, asymmetric information, moral hazard, learning and information sharing models.
We study competitive nonlinear pricing in a model involving simultaneously horizontal and vertical product differentiation. It is a particular case of a more general model of optimal contracting with uncertain participation that we study elsewhere (Rochet-Stole (1997)).
