A decentralized route to the origins of scaling in human language

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 $-1$. Previous work has stressed that this pattern arises from a conflict of interests of the participants of communication. The challenge here is to define a computational multi-agent language game, mainly based on a parameter that measures the relative participant's interests. Numerical simulations suggest that at critical values of the parameter a human-like vocabulary, exhibiting scaling properties, seems to appear. The appearance of an intermediate distribution of frequencies at some critical values of the parameter suggests that on a population of artificial agents the emergence of scaling partly arises as a self-organized process only from local interactions between agents.