We investigate a society with two official languages: A, shared by all individuals and B, spoken by a bilingual minority. 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 show 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.
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