Abstract
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 spheres of legislation as context and learn an influence network for each sphere. Second, how do we analyze these networks 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 structural centrality measures fail to capture.
Highlights
In recent times, the study of social influence has extended beyond mathematical sociology [16, 24, 50] and has entered the realm of computation [1, 4,5,6,7, 28, 30, 33, 34, 36, 37]
Game‐theoretic vs. structural centrality measures In the above game-theoretic formulation of most influential nodes, we find that each set of most influential senators across all spheres is comprised of an equal
Our analysis shows that contrary to the popular notion that the U.S Congress is overly polarized these days, the measure of polarization varies according to the spheres of legislation
Summary
The study of social influence has extended beyond mathematical sociology [16, 24, 50] and has entered the realm of computation [1, 4,5,6,7, 28, 30, 33, 34, 36, 37]. We learn the linear influence game (LIG) models, analyze influence networks, compute equilibria, and find most influential senators for each sphere separately. If all influence weights and threshold levels are 0 (i.e., W = 0, b = 0), all 2n possible joint actions among n players would be PSNE, trivially covering all observed voting data. This is undesirable as it has no predictive power at all. 0 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010 ρ ρ vs. Error (Best Response)
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