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URL: http://arxiv.org/pdf/cond-mat/0603205

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Authoritative: http://dx.doi.org/10.1209/epl/i2005-10481-7   (Publisher's PDF... likely be available here.)

Source: http://arxiv.org/abs/cond-mat/0603205

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Abstract

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 $p \gg 1/N$ 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.

@article{dallasta06agreementDynamicsSmallWorld,
  author={L. Dall'Asta and A. Baronchelli and A. Barrat and V. Loreto},
  title={Agreement dynamics on small-world networks},
  journal={Europhysics Letters},
  year={2006},
  volume={73},
  number={6},
  pages={969-975},
  doi={10.1209/epl/i2005-10481-7},
  url={http://www.isrl.uiuc.edu/~amag/langev/paper/dallasta06agreementDynamicsSmallWorld.html}
}

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