To help predict whether the proliferation of free trade agreements (FTAs) continues until global free trade is effectively attained, this paper investigates dynamic paths of FTAs, generated by numerical simulations of a model of an FTA network formation game with many countries. The characteristics of the final FTA network naturally depend on how the proposer of an FTA is chosen in each period. The paper finds that if the country that has the largest incentive to form an FTA is chosen as a proposer in each period, the network evolution always leads to a unique final FTA network, which may or may not be the complete network of FTAs. FTA networks often evolve to a partition of the world into a small number of groups of asymmetric size owing to the negative network externality caused by preference erosion.