The aim here is double: within a bipartite-graph approach to human vocabularies, to propose a decentralized language game model for the formation of Zipfian properties.
The Zipf's law establishes that if the words of a (large) text are ordered by decreasing frequency, the frequency versus the rank decreases as a power law with exponent close to $-1$.
Traditionally, the formation of vocabularies 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 work develops a computational model (by Automata Networks) of phonological similarity effects involved in the formation of word-meaning associations on artificial populations of speakers.
Finally, computer simulations are explored in two-dimensional lattices with the purpose to recover the main features of the Naming Game and to describe the dynamics under different updating schemes.