Strategic Formation of Homogeneous Bargaining Networks

We analyze a model of strategic network formation prior to a Manea (2011) bargaining game: ex-ante homogeneous players form an undirected network with explicit linking costs anticipating expected equilibrium payoffs from the subsequent sequential network bargaining. Assuming patient players, we provide a complete characterization of networks being pairwise (Nash) stable on a cost interval of positive length: specific disjoint unions of separated pairs, odd circles and isolated players constitute this class. Even for all single cost levels we are able to exclude a wide range of structures from being pairwise stable, including all other equitable networks. As an important implication, this reveals the diversity of possible bargaining outcomes to be substantially narrowed down provided pairwise stability. Further, we find that for sufficiently high costs the pairwise stable and efficient networks coincide whereas this does not hold if costs are low or at an intermediate level. As a robustness check, we also study the case of time-discounting players.