Agreement dynamics on interaction networks with diverse topologies

Alain Barrat (1, 2) , Andrea Baronchelli (3) , Luca Dall'Asta (1) , Vittorio Loreto (3)

1 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
2 Complex Networks Lagrange Laboratory
3 Dipartimento di Fisica

We review the behavior of a recently introduced model of agreement dynamics, called the Naming Game. This model describes the self-organized emergence of linguistic conventions and the establishment of simple communication systems in a population of agents with pairwise local interactions. The mechanisms of convergence towards agreement strongly depend on the network of possible interactions between the agents. In particular, the mean-field case in which all agents communicate with all the others is not efficient, since a large temporary memory is requested for the agents. On the other hand, regular lattice topologies lead to a fast local convergence but to a slow global dynamics similar to coarsening phenomena. The embedding of the agents in a small-world network represents an interesting trade-off: a local consensus is easily reached, while the long-range links allow to bypass coarsening-like convergence. We also consider alternative adaptive strategies which can lead to faster global convergence.

Domaines: Mécanique statistique [cond-mat.stat-mech]

Alain Barrat, Andrea Baronchelli, Luca Dall'Asta, Vittorio Loreto. Agreement dynamics on interaction networks with diverse topologies. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2007, 17, pp.026111. ⟨10.1063/1.2734403⟩. ⟨hal-00165343⟩