Coalitional Bargaining in Networks

We analyze a noncooperative bargaining game with a general coalition structure. In each period an opportunity for a feasible coalition to form arises according to a stochastic process, and a randomly selected agent in the coalition makes a take-it-or-leave-it offer to the other agents in the coalition. We develop a new technique based on convex programming to characterize the unique stationary equilibrium payoff of the game. We apply the framework to various settings including trading networks with middlemen and cooperation networks with overlapping communities. In these applications, feasible coalitions are determined by an underlying network structure. We study the effect of the underlying network on the pattern of trade and show how an agent's payoff is related to her position in the network.