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Topology Induced Coarsening in Language Games

A. Baronchelli·L. Dall'Asta·A. Barrat·V. Loreto
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Abstract

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 which requires less cognitive effort of the agents, with respect to the mean-field case, but takes longer to complete. In 1-d 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 N^{1+2/d} in dimension d<5 (d=4 being the upper critical dimension), while in mean-field both memory and time scale as N^{3/2}, for a population of N agents. We present analytical and numerical evidences supporting this picture.

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A. Baronchelli, L. Dall'Asta, A. Barrat, V. Loreto. 2005-12-06. Topology Induced Coarsening in Language Games. https://doi.org/10.1103/physreve.73.015102

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