Journal
EUROPHYSICS LETTERS
Volume 73, Issue 6, Pages 969-975Publisher
IOP Publishing Ltd
DOI: 10.1209/epl/i2005-10481-7
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In this paper we analyze the effect of a non-trivial topology on the dynamics of the so-called Naming Game, a recently introduced model which addresses the issue of how shared conventions emerge spontaneously in a population of agents. We consider in particular the small-world topology and study the convergence towards the global agreement as a function of the population size N as well as of the parameter p which sets the rate of rewiring leading to the small-world network. As long as p >> 1/ N, there exists a crossover time scaling as N/p(2) which separates an early one-dimensional-like dynamics from a late-stage mean-field-like behavior. At the beginning of the process, the local quasi-one-dimensional topology induces a coarsening dynamics which allows for a minimization of the cognitive effort (memory) required to the agents. In the late stages, on the other hand, the mean-field-like topology leads to a speed-up of the convergence process with respect to the one-dimensional case.
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