On Influence, Stable Behavior, and the Most Influential Individuals in Networks: A Game-Theoretic Approach
Abstract
We introduce a new approach to the study of influence in strategic settings where the action of an individual depends on that of others in a network-structured way. We propose influence games as a game-theoretic model of the behavior of a large but finite networked population. Influence games allow both positive and negative influence factors, permitting reversals in behavioral choices. We embrace pure-strategy Nash equilibrium (PSNE), an important solution concept in non-cooperative game theory, to formally define the stable outcomes of an influence game and to predict potential outcomes without explicitly considering intricate dynamics. We address an important problem in network influence, the identification of the most influential individuals, and approach it algorithmically using PSNE computation. Computationally, we provide (a) complexity characterizations of various problems on influence games; (b) efficient algorithms for several special cases and heuristics for hard cases; and (c) approximation algorithms, with provable guarantees, for the problem of identifying the most influential individuals. Experimentally, we evaluate our approach using both synthetic influence games as well as several real-world settings of general interest, each corresponding to a separate branch of the U.S. Government. Mathematically, we connect influence games to important game-theoretic models: potential and polymatrix games.