  Zipf's law establishes a scaling behavior for word-frequencies in large text
corpora. The appearance of Zipfian properties in human language has been
previously explained as an optimization problem for the interests of speakers
and hearers. On the other hand, human-like vocabularies can be viewed as
bipartite graphs. 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. To do this, we define a language game, in
which a population of artificial agents is involved in idealized linguistic
interactions. Numerical simulations show the appearance of a phase transition
from an initially disordered state to three possible phases for language
formation. Our results suggest that Zipfian properties in language seem to
arise partly from decentralized linguistic interactions between agents endowed
with bipartite word-meaning mappings.
