**Abstract:** Traditionally, the formation of vocabularies has been studied by agent-based models (primarily, the naming game) in which random pairs of agents negotiate word-meaning associations at each discrete time step. This article proposes a first approximation to a novel question: To what extent is the negotiation of word-meaning associations influenced by the order in which agents interact? Automata networks provide the adequate mathematical framework to explore this question. Computer simulations suggest that on two-dimensional lattices the typical features of the formation of word-meaning associations are recovered under random schemes that update small fractions of the population at the same time; by contrast, if larger subsets of the population are updated, a periodic behavior may appear.