Limitation of Efficiency: Strategy-Proofness and Single-Peaked Preferences with Many Commodities

In this paper, we study a resource allocation problem of economies with many commodities and single-peaked preferences. It is known that the uniform rule is the unique allocation mechanism satisfying strategy-proofness, Pareto efficiency and anonymity, if the number of good is only one and pereferences are single-peaked. (Sprumont [7].) However, if the number of goods is greater than one, the situation drastically changes and a tradeoff between efficiency and strategy-proofness arises. The generalized uniform rule in multiple-commodity settings is still starategy-proof, but not Pareto efficient in general. In this paper, we show that in a class of all strategy-proof mechanisms the generalized uniform rule is a ”second best” strategy-proof mechanism in that there is no other strategy-proof mechanism which gives a ”better” outcome than the generalized uniform rule in terms of Pareto domination.