  We examine the evolution of the vocabulary of a group of individuals
(linguistic agents) on a scale-free network, using Monte Carlo simulations and
assumptions from evolutionary game theory. It is known that when the agents are
arranged in a two-dimensional lattice structure and interact by diffusion and
encounter, then their final vocabulary size is the maximum possible. Knowing
all available words is essential in order to increase the probability to
``survive'' by effective reproduction. On scale-free networks we find a
different result. It is not necessary to learn the entire vocabulary available.
Survival chances are increased by using the vocabulary of the ``hubs'' (nodes
with high degree). The existence of the ``hubs'' in a scale-free network is the
source of an additional important fitness generating mechanism.
