Game-theoretic models of influence in networks often assume the network structure to be static. In this paper, we allow the network structure to vary according to the underlying behavioral context. This leads to several interesting questions on two fronts. First, how do we identify different contexts and learn the corresponding network structures using real-world data? We focus on the U.S. Senate and apply unsupervised machine learning techniques, such as fuzzy clustering algorithms and generative models, to identify different spheres of legislation as context and learn an influence network for each sphere. Second, how do we analyze these networks in order to gain an insight into the role played by the spheres of legislation in various interesting constructs like polarization and most influential nodes? To this end, we apply both game-theoretic and social network analysis techniques. In particular, we show that game-theoretic notion of most influential nodes brings out the strategic aspects of interactions like bipartisan grouping, which typical centrality measures fail to capture. We also show that for the same set of senators, some spheres of legislation are more polarizing than others.
Phillips, Andrew C.; Irfan, Mohammad T.; and Ostertag-Hill, Luca, "Spheres of Legislation: Polarization and Most Influential Nodes in Behavioral Context" (2020). DCS Faculty Publications. 15.