Nicolas Fraiman, Tzu-Chi Lin, Mariana Olvera-Cravioto
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引用次数: 0
Abstract
We propose and analyze a mathematical model for the evolution of opinions on directed complex networks. Our model generalizes the popular DeGroot and Friedkin-Johnsen models by allowing vertices to have attributes that may influence the opinion dynamics. We start by establishing sufficient conditions for the existence of a stationary opinion distribution on any fixed graph, and then provide an increasingly detailed characterization of its behavior by considering a sequence of directed random graphs having a local weak limit. Our most explicit results are obtained for graph sequences whose local weak limit is a marked Galton-Watson tree, in which case our model can be used to explain a variety of phenomena, for example, conditions under which consensus can be achieved, mechanisms in which opinions can become polarized, and the effect of disruptive stubborn agents on the formation of opinions.Funding: This work was supported by the National Science Foundation [Grants NSF-DMS-1929298 and CMMI-2243261].
期刊介绍：
Mathematics of Operations Research is an international journal of the Institute for Operations Research and the Management Sciences (INFORMS). The journal invites articles concerned with the mathematical and computational foundations in the areas of continuous, discrete, and stochastic optimization; mathematical programming; dynamic programming; stochastic processes; stochastic models; simulation methodology; control and adaptation; networks; game theory; and decision theory. Also sought are contributions to learning theory and machine learning that have special relevance to decision making, operations research, and management science. The emphasis is on originality, quality, and importance; correctness alone is not sufficient. Significant developments in operations research and management science not having substantial mathematical interest should be directed to other journals such as Management Science or Operations Research.
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