Second-language acquisition behavior and hegemonic language

We construct a game-theoretic model in which there are multiple countries with their own languages and each citizen can gain from additional communication in her secondarily acquired language. We demonstrate that in any equilibrium, a hegemonic language, which is a language that all citizens in other countries want to study, emerges. Such an equilibrium is more likely to exist if the size of the population of a country that is not the largest increases, or if the ratio of the gain from the additional communication in the second language to the cost of acquisition increases.