Are trade blocs conducive to free trade?

Is integration conducive to free trade equilibria? In the context of an infinitely repeated tariff-setting game with intraindustry trade, integration of numerous very small provinces promotes free trade by deterring the exercise of market power by a large dominant province. If the dominant province is smaller than the rest of the world combined, integration promotes free trade if it results in multiple equal-sized blocs. Free trade is less likely the higher the degree of integration in such a world, but it is always more likely than in a world with one very dominant trading partner.