Self-organization of vocabularies under different interaction orders

Traditionally, the formation of linguistic conventions has been studied by agent-based models (specially, the Naming Game) in which random pairs of agents negotiate word-meaning associations at each discrete time step. This paper proposes a first approximation to a novel question: To what extent the negotiation of word-meaning associations is influenced by the order in which the individuals interact? Automata Networks provide the adequate mathematical framework to explore this question. A theoretical result shows that if all individuals are updated at the same time a periodic behavior may appear. Computer simulations suggest that on two-dimensional lattices the typical features of the formation of linguistic conventions are recovered under random schemes that update small fractions of the population at the same time.