Optimizing Social Welfare in Social Networks

Abstract

We study the computational complexity of envy minimization and maximizing the social welfare of graph-envy-free allocations in social networks. Besides the already known \\(\\mathrm {NP}\\)-completeness of finding allocations with maximal utilitarian social welfare we prove that \\(\\mathrm {NP}\\)-completeness is in general also given for the egalitarian social welfare and the Nash product. Moreover, we focus on an extended model, based on directed social relationship graphs and undirected social trading graphs, and analyze the computational complexity of reaching a graph-envy-free allocation by trades with so-called don’t care agents and without money.