On the manipulability of efficient exchange rules

There is a divisible commodity and money. Each agent has an endowment of the two goods and continuous, monotone, convex preferences over bundles. Agents may benefit from trade. An exchange rule is a mapping that, for each profile of preferences, calculates for each agent a trade that he finds acceptable, given his preferences. It is known that no strategy-proof exchange rule always yields Pareto efficient outcomes. Strategy-proofness, however, is quite strong. We may instead ask: if we insist upon Pareto efficiency, how frequently will the exchange rule be manipulable? We identify a large subdomain, D, of quasilinear economies on which any efficient exchange rule will be densely manipulable. Moreover, we show the set of manipulable economies is non-meagre. For generic economies outside of D, there exist rules that are locally non-manipulable.