Inequality and network structure

We explore the manner in which the structure of a social network constrains the level of inequality that can be sustained among its members, based on the following considerations: (i) any distribution of value must be stable with respect to coalitional deviations, and (ii) the network structure itself determines the coalitions that may form. We show that if players can jointly deviate only if they form a clique in the network, then the degree of inequality that can be sustained depends on the cardinality of the maximum independent set. For bipartite networks, the size of the maximum independent set fully characterizes the degree of inequality that can be sustained. This result extends partially to general networks and to the case in which a group of players can deviate jointly if they are all sufficiently close to each other in the network. ► This paper studies how the structure of a social network constrains the level of inequality that can be sustained. ► If a group of players in a network can deviate only when they are directly connected, a key determinant is the size of the maximum independent set of the network. ► In bipartite networks, the size of the maximum independent set fully characterizes the maximum level of inequality that can be sustained. ► A partial characterization is provided for general networks.