  We study the recently introduced Bayesian naming game model, in which the
one-shot learning of the minimal naming game is replaced by a more realistic
learning process defined according to Bayesian inference. The results are
compared with those obtained from the minimal naming game model. We focus on
the dynamics of the bilingual population, providing analytical estimates of the
upper bound for the number of bilinguals in both models based on the mean-field
equations, and validate them through numerical simulations of the multi-agent
models. We show that in the Bayesian model the maximum number of bilinguals is
always lower with respect to the minimal naming game and that the two models
are characterized by qualitatively different time evolutions.
