Minority Language and the Stability of Bilingual Equilibria

We investigate a society with two official languages: A, shared by all individuals and B, spoken by a bilingual mirority. Thus, it is only B that needs t increase its population share, and therefore, only the language dynamics that derive from the intearctions that occur inside the bilingual population are both empirically and theoretically relevant. To this end, a model is developed in which the bilingual agents must make strategic decisions about the language to be used in a conversation. Decisions are taken under imperfect information about the linguistic type of the participants in the interaction. We first study all the posible equilibria the model might produce and the language used in each of them. Then, in a dynamic setting, we study the building of a language convention by the bilingual speakers. The main result is that there is a mixed strategy Nash equilibrium in which bilingual agents use both the A and B languages. This equilibrium is evolutionary stable, and dynamically, it is asymptotically stable for the one-population replicator dynamics. In this equilibrium, the use of B between bilingual individuals could be very low.Nagore Iriberri acknowledges financial support from Ministerio de Educación y Ciencia (SEJ2006-05455 and SEJ2007-64340) and the support of the Barcelona GSE Research Network and of the Government of Catalonia. José Ramón Uriarte gratefully acknowledges the financial support from the Spanish Ministry of Science and Technology and FEDER, grant number SEJ 2006-05455, and the University of the Basque Country, UPV 00043.321-15836/2004