Inefficiency of strategy-proof allocation mechanisms in pure exchange economies

In this paper I prove that in the standard model of 2×n (n2) pure exchange economies there is no allocation mechanism that is efficient, non-inversely-dictatorial, and strategy-proof. This strengthens two previous results on this subject by Hurwicz and by Dasgupta, Hammond, and Maskin.I thank Alvin Klevorick, William Thomson, and an anonymous referee of the journal for many helpful comments.