The Role of bilinguals in the Bayesian naming game

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.