Price Competition under Limited Supply

This note investigates the standard Bertrand-Edgeworth duopolistic competition in which two firms sell a homogenous good and have an identical capacity constraint. We examine three firstcome, first-served rationing rules: a) high-to-low rationing where customers arrive in decreasing order of willingness to pay, b) proportional rationing where customer arrivals are independent of willingness to pay, and c) low-to-high rationing where customers arrive in increasing order of willingness to pay. The third rationing rule is new and analyzed here the first-time. Unlike the high-to-low and the proportional rationing rules, the low-to-high rationing rule has no pure-strategy Nash equilibrium. There exists however a symmetric mixed-strategy equilibrium. Since the low-to-high rationing rule leads to less competitive outcomes, firms can reduce the degree of price competition by influencing the order of customer arrivals. Subject classifications: marketing: competitive strategy, pricing, promotion. Area of review : Marketing. ∗We thank Eric Maskin for his insightful comments. Tony H. Cui is an Assistant Professor of Marketing at the Carlson School of Management, University of Minnesota. Teck H. Ho is William Halford Jr. Family Professor of Marketing at the Haas School of Business, University of California, Berkeley. Authors contributed equally and are listed in alphabetical order.