We study a Rubinstein-Stahl two-player non-cooperative bargaining game played by n players connected in a communication network. We allow the players to communicate with any peer in the same component via the existing paths connecting the peers in a given communication network (global interaction). The unique stationary subgame perfect equilibrium profile characterizes the players’ expected payoff as function of their betweenness centrality score. Secondly, we study a dynamic link-formation game which allows the players to activate new linkages or sever existing ones in order to increase their bargaining power for a given marginal cost per link. We identify the conditions under which the resultant pairwise stable network structures belong to the family of the nested split graphs.