On Influence, Stable Behavior, and the Most Influential Individuals in Networks: A Game-Theoretic Approach
Mohammad T. Irfan, Luis E. Ortiz
备注：
Accepted to AI Journal, subject to addressing the reviewers' points (which are addressed in this version). An earlier version of the article appeared in AAAI-11
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 \emph{influence games} as a \emph{game-theoretic} model of the behavior of a large but finite networked population. Influence games allow \emph{both} positive and negative \emph{influence factors}, permitting reversals in behavioral choices. We embrace \emph{pure-strategy Nash equilibrium (PSNE)}, an important solution concept in non-cooperative game theory, to formally define the \emph{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 \emph{most influential individuals}, and approach it algorithmically using PSNE computation. \emph{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. \emph{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. \emph{Mathematically,} we connect influence games to important game-theoretic models: \emph{potential and polymatrix games}.
The influential work of Bravo et al. 2018 shows that derivative free play in strongly monotone games has complexity $O(d^2/\varepsilon^3)$, where $\varepsilon$ is the target accuracy on the expected squared distance to the solution. This note shows that the efficiency estimate is actually $O(d^2/\varepsilon^2)$, which reduces to the known efficiency guarantee for the method in unconstrained optimization. The argument we present simple interprets the method as stochastic gradient play on a slightly perturbed strongly monotone game.
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DeepMind（深度思维）；University College London（伦敦大学学院）；Google（谷歌）；Carnegie Mellon University（卡内基梅隆大学）
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Isfahan University of Technology（伊斯法罕理工大学）；University of Arizona（亚利桑那大学）
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University of Michigan（密歇根大学）；Bilkent University（比尔肯特大学）
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Institute for Information Transmission Problems, Russian Academy of Sciences（俄罗斯科学院信息传输问题研究所）
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