The paper argues that language change can be explained through the stochasticity observed in real-world natural language use. This thesis is demonstrated by modeling language use through language games played in an evolving population of agents. We show that the artificial languages which the agents spontaneously develop based on self-organisation, do not evolve even if the population is changing. Then we introduce stochasticity in language use and show that this leads to a constant innovation (new forms and new form-meaning associations) and a maintenance of variation in the population, if the agents are tolerant to variation. Some of these variations overtake existing linguistic conventions, particularly in changing populations, thus explaining lexicon change.