Language evolution in finite populations

We study a simple game-theoretical model of language evolution in finite populations. This model is of particular interest due to a surprising recent result for the infinite population case: under replicator dynamics, the population game converges to socially inefficient outcomes from a set of initial conditions with non-zero Lesbegue measure. If finite population models do not exhibit this feature then support is lent to the idea that small population sizes are a key ingredient in the emergence of linguistic coherence. It has been argued elsewhere that evolution supports efficient languages in finite populations using the method of comparing fixation probabilities of single mutant invaders to the inverse of the population size. We instead analyze an alternative generalization of replicator dynamics to finite populations that leads to the emergence of linguistic coherence in an absolute sense. After a long enough period of time, linguistic coherence is observed with arbitrarily high probability as a mutation rate parameter is taken to zero. We also discuss several variations on our model.