Evolution of a Collusive Price in a Networked Market

This paper studies evolution of firms' behavior in a networked Bertrand oligopoly market, in which firms who are located on vertices of a network compete in price with their neighbors. This network model is also applied to a market with multi-dimensionally differentiated products. In a non-networked market, it is known that the Bertrand-Nash equilibrium pricing is evolutionarily stable. We show, however, that in our large networked market, the Bertrand-Nash equilibrium price is not stable but a collusive price is evolutionarily stable under weak selection. As the magnitude of transportation cost increases, firms charge a more collusive price in the long run. The results suggest that collusive pricing prevails in a large market if and only if it is networked