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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}

MSC:
91A43 Games involving graphs
60G50 Sums of independent random variables; random walks
05C81 Random walks on graphs
91B69 Heterogeneous agent models
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References:
[1] DOI: 10.1103/RevModPhys.81.591
[2] DOI: 10.1142/S0129183108012297 · Zbl 1141.91668
[3] DOI: 10.1142/S0129183107011789 · Zbl 1151.91076
[4] Pan X., Complex Syst. Complex Sci. 6 pp 87– (2009)
[5] DOI: 10.1080/0022250X.1971.9989794 · Zbl 1355.91061
[6] Axelrod R. M., The Complexity of Cooperation (1997) · Zbl 0904.90182
[7] Epstein J. M., Growing Artificial Societies: Social Science from the Bottom Up (1996)
[8] Challet D., Minority Games: Interacting Agents in Financial Markets (2005) · Zbl 1053.91001
[9] DOI: 10.1103/PhysRevLett.92.058701
[10] DOI: 10.1109/MCSE.2005.114 · Zbl 05092612
[11] DOI: 10.2189/asqu.52.4.667
[12] DOI: 10.1103/PhysRevA.45.1067
[13] DOI: 10.1103/PhysRevE.53.R3009
[14] DOI: 10.1103/PhysRevE.53.3078
[15] DOI: 10.1103/PhysRevLett.87.045701
[16] DOI: 10.1103/PhysRevE.77.016111
[17] DOI: 10.1007/s11403-009-0057-7
[18] DOI: 10.1103/PhysRevE.71.066107
[19] DOI: 10.1103/PhysRevE.74.036105
[20] DOI: 10.1162/artl.1995.2.3.319
[21] DOI: 10.1088/0305-4470/39/48/002 · Zbl 1107.68502
[22] DOI: 10.1103/PhysRevE.73.015102
[23] DOI: 10.1142/S0129183108012522 · Zbl 1153.82338
[24] Gonzalez-Avella J. C., J. Artif. Soc. Soc. Simul. 10 pp 9– (2007)
[25] DOI: 10.1142/S0129183107011492 · Zbl 1200.91260
[26] DOI: 10.1016/j.physa.2007.03.034
[27] DOI: 10.1088/1751-8113/41/43/435003 · Zbl 1151.82386
[28] DOI: 10.1140/epjb/e2003-00278-0
[29] DOI: 10.1103/PhysRevE.77.041121
[30] DOI: 10.1140/epjb/e2009-00284-2 · Zbl 1188.91142
[31] DOI: 10.1007/978-1-4613-8542-4
[32] DOI: 10.1007/978-1-4757-3124-8_7
[33] DOI: 10.1103/PhysRevE.83.046103
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