The economics of minority language use: theory and empirical evidence for a language game model

Language and cultural diversity is a fundamental aspect of the present world. We study three modern multilingual societies -- the Basque Country, Ireland and Wales -- which are endowed with two, linguistically distant, official languages: $A$, spoken by all individuals, and $B$, spoken by a bilingual minority. In the three cases it is observed a decay in the use of minoritarian $B$, a sign of diversity loss. However, for the "Council of Europe" the key factor to avoid the shift of $B$ is its use in all domains. Thus, we investigate the language choices of the bilinguals by means of an evolutionary game theoretic model. We show that the language population dynamics has reached an evolutionary stable equilibrium where a fraction of bilinguals have shifted to speak $A$. Thus, this equilibrium captures the decline in the use of $B$. To test the theory we build empirical models that predict the use of $B$ for each proportion of bilinguals. We show that model-based predictions fit very well the observed use of Basque, Irish, and Welsh.