Minority language and the stability of bilingual equilibria

Abstract

We investigate a society with two o¢ cial languages: A, shared by all individuals and B, spoken by a bilingual minority. Thus, it is only B that needs to increase its population share, and therefore, only the language dynamics that derive from the interactions 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 …rst study all the possible 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.2

The Role of Bilinguals in Language Competition

“…Despite most sociolinguistic surveys take these variables into account, on the level of data processing and mathematical modeling the situation is different and this aspect is rarely studied. This is best done in the framework of game-theoretical models, see e.g., [10,18].…”

Allee optimal control of a system in ecology

“…The model is also relevant in many applications in social behaviour studies. It may be viewed as a diffusive version of the game theoretical and ODE models introduced in [42] for minority languages. Traveling wave solutions linking the two stable equilibria play an essential role in the dynamical behaviour of these systems since they describe how, as time evolves, space domains that are occupied by the configuration y ∼ 1 tend towards the other stable value y ∼ 0 or vice-versa.…”

On the Emergence of Bilingualism in a Communication “All” Task as a Result of Competition Between Social Conformism and Language Simplification

“…In this work we are interested in the resulting evolution of a situation of language contact, not in the whole evolution process of emergence of bilingualism. This relates to the work of Iriberri and Uriarte (2013) who model the evolution of a mixed population of bilinguals and monolinguals and to the work of Lupyan and Dale (2010) who surveyed the influence of social structures on languages.…”

“…One of the issues is that many signaling conventions can arise simultaneously, requiring bilingual agents for the stability of a global communication system. Models that account for bilingualism have been developed recently, see for example (Burkett & Griffiths, 2010) or (Thompson, Roberts, & Smith, 2013) for Bayesian models, see also (Roberts, 2013), and (Iriberri & Uriarte, 2013) for a game theoretic model.…”