Innovation and Horizontal Differentiation in a Continuous-Time Hotelling Model

Abstract

We study the relationship between innovation and horizontal differentiation in a continuous-time dynamic duopoly. At any instant firms compete in prices in a Hotelling game. They may be differentiated both in terms of product quality (for which consumers have homogeneous tastes) and product location (for which tastes are heterogeneous). We consider in turn: (a) a game in which firms invest to improve quality (with fixed locations), and (b) a game in which they invest to relocate products (with an exogenous rate of quality improvement). Spillovers keep the interfirm quality differential from becoming too large. Symmetric Markov-perfect equilibria in the game with fixed locations show a relationship between taste heterogeneity and quality improvement that is U-shaped, in contrast with previous literature. In the game of endogenous product locations we show conditions for uniqueness of the symmetric MPE, and use this result to examine long-run impacts of changes in parameters, e.g., in the costs of product relocation.