We consider the allocation of goods in exchange economies with a finite number of agents who may have private information about their preferences. In such a setting, standard allocation rules such as Walrasian equilibria or rational expectations equilibria are not compatible with individual incentives. We characterize the set of allocation rules which are incentive compatible, or in other words, the set of strategy-proof social choice functions. Social choice functions which are strategy-proof are those which can be obtained from trading according to a finite number of pre-specified proportions. The number of proportions which can be accommodated is proportional to the number of agents. Such rules are necessarily inefficient, even in the limit as the economy grows.