Is the result that equilibrium trading outcomes are e cient in mar- kets without frictions robust to a scenario where agents' beliefs and plans aren't already aligned at their equilibrium values? In this pa- per, starting from a situation where agents' beliefs and plans aren't already aligned at their equilibrium values, we study whether out-of- equilibrium trading converges to e cient allocations. We show that out-of-equilibrium trading does converge with probability 1 to an e - 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 essen- tial to achieve gains from trade. We prove that experimentation does converge with probability 1 to an e cient allocation and the speed of convergence remains exponential with Cobb-Douglass utility functions.