A convention can be seen as a way of resolving a coordination problem. If different conventions exist in various geographical, social or other entities (called “groups”) and if there is some mobility between these groups, which conventions, if any, will emerge as the successful ones? A simple evolutionary process is suggested and it is shown that the process converges to a Nash equilibrium for all games satisfying weak acyclity. Further, if the process converges, it converges to an efficient convention for all games in which the Pareto optimal symmetric equilibria are strict. Hence, the paper presents an explanation for the endogenous evolution of efficiency. In contrast to most recent studies in evolutionary game theory, the conclusions do not rely on random “mutations”. Instead, the driving force is the tendency of players to have increased interaction with member of their own group (viscosity).