Strategic Formation of Customer Relationship Networks

We analyze the stability of networks when two intermediaries strategically form costly links to customers. We interpret these links as customer relationships that enable trade to sell a product. Equilibrium prices and equilibrium quantities on the output as well as on the input market are determined endogenously for a given network of customer relationships. We investigate in how far the substitutability of the intermediaries' products and the costs of link formation influence the intermediaries' equilibrium profits and thus have an impact on the incentives to strategically form relationships to customers. For networks with three customers we characterize locally stable networks, in particular existence is guaranteed for any degree of substitutability. Moreover for the special cases of perfect complements, independent products and perfect substitutes, local stability coincides with the stronger concept of Nash stability. Additionally, for networks with n customers we analyze stability regions for selected networks and determine their limits when n goes to infinity. It turns out that the shape of the stability regions for those networks does not significantly change compared to a setting with a small number of customers.