Baronchelli, A., Dall'Asta, L., Barrat, A. & Loreto, V. (2006). Topology-induced coarsening in language games. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 73(1), doi: 10.1103/PhysRevE.73.015102
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We investigate how very large populations are able to reach a global consensus, out of local “microscopic” interaction rules, in the framework of a recently introduced class of models of semiotic dynamics, the so-called naming game. We compare in particular the convergence mechanism for interacting agents embedded in a low-dimensional lattice with respect to the mean-field case. We highlight that in low dimensions consensus is reached through a coarsening process that requires less cognitive effort of the agents, with respect to the mean-field case, but takes longer to complete. In one dimension, the dynamics of the boundaries is mapped onto a truncated Markov process from which we analytically computed the diffusion coefficient. More generally we show that the convergence process requires a memory per agent scaling as N and lasts a time N1+2∕d in dimension d⩽4 (the upper critical dimension), while in mean field both memory and time scale as N3∕2, for a population of N agents. We present analytical and numerical evidence supporting this picture.
|Subjects:||Q Science > QC Physics|
|Divisions:||School of Engineering & Mathematical Sciences > Department of Mathematical Science|
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