Bargaining Dynamics and Varied Linking Costs in Stable Networks

n a scenario featuring two distinct player types, we examine the pairwise stability of stationary networks where agents engage in infinite-horizon bargaining games akin to Manea's framework. Link formation and maintenance costs are contingent upon communication ease and complementarities, with connections between individuals of different types becoming less expensive when complementarities are sufficiently strong. In such instances, various bipartite components emerge as stable, characterized by a lack of direct connections between players of the same type. These components exhibit inequitable disributions of surplus, resulting in asymmetric splits among linked individuals. This contrasts with scenarios where connections between individuals of the same type are less costly, leading to predominantly equitable stable components. OUr findings highlight how complementarities and the relative scarcity of certain types can influence the fairness of bargaining outcomes within networks.