Nesting Vertical and Horizontal Differentiation in Two-Sided Markets

We develop a model that is a synthesis of the two-sided markets duopoly model of Armstrong (2006) with the nested vertical and horizontal dierentiation model of Gabszewicz and Wauthy (2012), which consists of a linear city with dierent consumer densities on the left and on the right side of the city. In equilibrium, the high-quality platform sells at a higher price and captures a greater market share than the low-quality platform, despite the indifferent consumer being closer to the high-quality platform. The difference between market shares is lower than socially optimal, because of the inter-group externality and because the high-quality platform sells at a higher price. We conclude that a perturbation that introduces a negligible dierence between the consumer density on the left and on the right side of the city may disrupt the existence of equilibrium in the model of Armstrong (2006). Finally, we show that inter-group externalities make it easier to deter an inferior-quality entrant and make it easier for a superior-quality entrant to conquer the market.