Network bargaining

We consider models for bargaining in social networks, in which players are represented by vertices and edges represent bilateral opportunities for deals between pairs of players. Each deal yields some fixed wealth if its two players can agree on how to divide it; otherwise it yields no wealth. In such a setting, Chakraborty and Kearns (WINE 2008) introduced a simple axiomatic model that stipulates an equilibrium concept in which all players are rationally satisfied with their shares. We further explore that equilibrium concept here. In particular, we give an FPTAS to compute approximate equilibrium in bipartite graphs. We also show that equilibrium is not unique, and give conditions that ensure uniqueness on regular graphs. Finally, we explore the effect of network structure on solutions given by our model, using simulation methods and statistical analysis.