Zipf's law establishes a scaling behavior for word frequencies in large text corpora. The appearance of Zipfian properties in vocabularies (viewed as an intermediate phase between referentially useless one-word systems and one-to-one word-meaning vocabularies) has been previously explained as an optimization problem for the interests of speakers and hearers. Remarkably, humanlike vocabularies can be viewed also as bipartite graphs. Thus, 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 drastic transition from an initially disordered state towards three kinds of vocabularies. Our results open ways to study Zipfian properties in language, reconciling models seeing communication as a global minima of information entropic energies and models focused on self-organization.