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 degrees of substitutability (edges). We also locate consumers into this network, so that the location of each consumer (node) corresponds to her “ideal” variety. We show that there exists a unique Bertrand-Nash equilibrium where prices are determined by both the firms' sign-alternating Bonacich centralities and the average willingness to pay across consumers. 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 central firm does not always enjoy higher monopoly power than the peripheral firms.