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 โ€œidealโ€ variety. We show that, even though prices need not to be strategic complements, there exists a unique Nash equilibrium in the price game among firms. Equilibrium prices are determined by both firmsโ€™ sign-alternating 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.

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Suggested citation: Ushchev, P., Y. Zenou, (2016), ‘Price Competition in Product Variety Networks’, Nota di Lavoro 59.2016, Milan, Italy: Fondazione Eni Enrico Mattei