Bargaining on Networks

We study an infinite horizon game in which pairs of players connected by a network are randomly matched to bargain over a unit surplus. We prove that for each discount factor all equilibria are payoff equivalent. The equilibrium payoffs and the set of equilibrium agreement links converge as players become increasingly patient. We construct an algorithm that determines the limit equilibrium payoffs by iterating the finding that players with extreme limit equilibrium payoffs form oligopoly subnetworks. An oligopoly subnetwork consists of a set of mutually estranged players and their bargaining partners; in equilibrium, for high discount factors, the partners act as an oligopoly for the mutually estranged players. In the equilibrium limit, surplus within an oligopoly subnetwork is divided according to the shortage ratio of the mutually estranged players with respect to their partners, with all players on each side receiving identical payoffs. The algorithm is used to characterize equitable networks, stable networks, and non-discriminatory buyerseller networks. The results extend to heterogeneous discount factors and general matching technologies.