  We examine a naming game on an adaptive weighted network. A weight of
connection for a given pair of agents depends on their communication success
rate and determines the probability with which the agents communicate. In some
cases, depending on the parameters of the model, the preference toward
successfully communicating agents is basically negligible and the model behaves
similarly to the naming game on a complete graph. In particular, it quickly
reaches a single-language state, albeit some details of the dynamics are
different from the complete-graph version. In some other cases, the preference
toward successfully communicating agents becomes much more relevant and the
model gets trapped in a multi-language regime. In this case gradual coarsening
and extinction of languages lead to the emergence of a dominant language,
albeit with some other languages still being present. A comparison of
distribution of languages in our model and in the human population is
discussed.
