Nash Equilibrium in Duopoly with Products Defined by Two Characteristics

Abstract

This article analyzes the analogue ofHotellingls duopoly model when products are dejned by two characteristics. Using the assumptions of the original model of Hotelling, we show that demand and projt functions are continuous for a wide class of utility functions. When the utilityfunction is linear in the Euclidean distance in the space of characteristics, a noncooperative equilibrium in prices exists for all symmetric locations ofjirms. This is in contrast to the result in the one-characteristic model where a noncooperative equilibrium exists only when products are very diferent. 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.