Is the result that equilibrium trading outcomes are efficient in markets without frictions robust to a scenario where agents’ beliefs and plans aren’t already aligned at their equilibrium values? In this paper, starting from a situation where agents’ beliefs and plans aren’t already aligned at their equilibrium values, we study whether out-ofequilibrium trading converges to efficient allocations. We show that out-of-equilibrium trading does converge with probability 1 to an effi- cient allocation even when traders have limited information and trade cautiously. In economies where preferences can be represented by Cobb-Douglass utility functions, we show, numerically, that the rate of convergence will be exponential. We show that experimentation leads to convergence in some examples where multilateral exchange is essential to achieve gains from trade. We prove that experimentation does converge with probability 1 to an efficient allocation and the speed of convergence remains exponential with Cobb-Douglass utility functions.