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 costly undirected links anticipating expected equilibrium payoffs from the subsequent network bargaining. Assuming patient players, we provide a complete characterization of non-singularly pairwise (Nash) stable networks: specific disjoint unions of separated pairs, odd circles and isolated players constitute this class. We also show that many generic structures are not even singularly pairwise stable. As an important implication, this reveals the diversity of possible bargaining outcomes to be substantially narrowed down provided pairwise stability. Further, 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.