@article{Dall, author = {Luca Dall'Asta and Andrea Baronchelli and Alain Barrat and Vittorio Loreto},journal = {EUROPHYSICS LETTERS},note = {language},pages = {969--975},publisher = {EDP Sciences},title = {Agreement dynamics on small-world networks},type = {article},volume = {73},year = {2006},url = {https://doi.org/10.1209/epl/i2005-10481-7},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 >> 1/N, there exists a crossover time scaling as N/P^2which 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.}}