Pairwise Influences and Bargaining Among the Many

In this paper we build a model to analyze distributional conflict when the utility of each agent is heterogeneously influenced by other agents’ utility. There are two dimensions of heterogeneity: who influences whom, and the strength of any such pairwise dependent influence. The pattern of bilateral influences takes the form of a weighted and directed network. Direct influences spread their effects through chains of connected agents in this network. We characterize the Nash bargaining solution and analyze how pairwise influences, and the indirect effects they generate, are internalized in shares and utilities obtained. The analysis relies on network centrality indexes that measure each agent’s prominence due to his position in the influences structure. Our results have implications for the study of urban crime, government spending, and bargaining with social preferences.