Price Competition in Product Variety Networks

We develop a product-differentiated model where the product space is a network defined as a set of varieties (nodes) linked by their degree of substituabilities (edges). In this network, we also locate consumers so that the location of each consumer (node) corresponds to her "ideal" variety. We show that there exists a unique Nash equilibrium in the price game among firms. Equilibrium prices are determined by firms' weighted Bonacich centralities and the average willingness to pay across consumers. They both hinge on the network structure of the firm-product space. We also investigate how local product differentiation and the spatial discount factor affect the equilibrium prices. We show that these effects non-trivially depend on the network structure. In particular, we find that, in a star-shaped network, the firm located in the star node does not always enjoy higher monopoly power than the peripheral firms.