Nash Equilibrium in Duopoly with Products Defined by Two Characteristics
Volume: Volume 17, No. 3
Issue: Autumn 1986
Pages: pp. 431-439
Authors: Nicholas Economides
Title: Nash Equilibrium in Duopoly with Products Defined by Two Characteristics
Abstract: This article analyzes the analogue of Hotelling's duopoly model when products are defined by two characteristics. Using the assumptions of the original model of Hotelling, we show that demand and profit functions are continuous for a wide class of utility functions. When the utility function is linear in the Euclidean distance in the space of characteristics, a noncooperative equilibrium in prices exists for all symmetric locations of firms. This is in contrast to the result in the one-characteristic model where a noncooperative equilibrium exists only when products are very different. The noncooperative equilibria are calculated and fully characterized. In contrast with the one-dimensional model of Hotelling, where equilibrium prices were constant irrespective of distance (of symmetric locations), here equilibrium prices tend to zero as the distance between products approaches zero.
JEL Classification
Microeconomics Theory of Firm and Industry under Imperfectly Competitive Market Structures (0226)
Theory of Regional Economics (9411)