Formation of Bargaining Networks Via Link Sharing

This paper presents a model of collusive bargaining networks. Given a status quo network, game is played in two stages: in the first stage, pairs of sellers form the network by signing two-sided contracts that allow sellers to use connections of other sellers; in the second stage, sellers and buyers bargain for the product. We extend the notion of a pairwise Nash stability with transfers to pairwise Nash stability with contracts and characterize the subgame perfect equilibria. The equilibrium rents are determined for all firms based on their collateral and bargaining power. When a stable equilibrium exists, sharing always generates maximum social welfare and eliminates the frictions created by the network structure. The equilibria depend on the initial network setup, likewise bargaining and contractual procedures. In the homogeneous case, equilibria exist when the number of buyers and sellers are relatively unequal. When the number of buyers exceeds number of sellers, bargaining privileges of sellers over buyers and a low sharing transfer are required for the equilibrium to exist. In the networks with relatively few monopolized sellers, sharing leads to a complete reallocation of surplus to sellers and a zero sharing transfer. When the global market is dominated by sellers, surplus is divided relatively equitably. It is also shown that in the special case of the model with only one monopolistic seller and no market entry, the sharing process organizes sellers in the supply chain order.