We consider a simple class of dynamic games. A continuum of players chooses between two actions (“locations”) in each period; per-period payoffs depend positively on the number of players choosing the same action. The resulting dynamics are investigated. If one location receives a favorable shock, the effects of the strength of externalities and the heterogeneity of the population on the extent of adjustment may be non-monotone and discontinuous, due to two competing effects. With stronger externalities (lower heterogeneity), less players move initially, but more players follow once the process has gained momentum.