Credible Nash Bargaining Solution for Bilateral Trading Networks

We study surplus division in network constrained bilateral matching markets with transferable utility. We introduce a new solution concept, the credible bargaining solution, which refines stability by requiring that, for each matched pair of buyer and seller, surplus be divided according to the Nash bargaining solution with respect to credible outside options, defined as their payoffs in some stable outcome of the submarket obtained by removing their link. We establish general properties of the credible bargaining solution, prove existence, and provide a complete characterization in the unit-surplus case based on the notion of essential links.