Social influencing and associated random walk models: asymptotic consensus times on the complete graph. (English) Zbl 1317.91007

Summary: We investigate consensus formation and the asymptotic consensus times in stylized individual- or agent-based models, in which global agreement is achieved through pairwise negotiations with or without a bias. Considering a class of individual-based models on finite complete graphs, we introduce a coarse-graining approach (lumping microscopic variables into macrostates) to analyze the ordering dynamics in an associated random-walk framework. Within this framework, yielding a linear system, we derive general equations for the expected consensus time and the expected time spent in each macro-state. Further, we present the asymptotic solutions of the 2-word naming game and separately discuss its behavior under the influence of an external field and with the introduction of committed agents.{
©2011 American Institute of Physics}


91A43 Games involving graphs
60G50 Sums of independent random variables; random walks
05C81 Random walks on graphs
91B69 Heterogeneous agent models
Full Text: DOI arXiv


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