Second-best Efficiency of Allocation Rules: Strategy-proofness and Single-peaked Preferences with Multiple Commodities∗

This paper studies the design of a strategy-proof resource allocation rule in economies with perfectly divisible multiple commodities and single-peaked preferences. It is known that the uniform rule is the unique allocation rule satisfying strategy-proofness, Pareto efficiency, and anonymity if the number of commodity is only one and preferences are single-peaked (Sprumont (1991)). However, if the number of commodities is greater than one, the situation drastically changes and a trade-off between strategy-proofness and Pareto efficiency arises. The generalized uniform rule in multiple-commodity settings is still strategy-proof, but not Pareto efficient. In this paper, we first investigate the existence problem of second-best efficient rules, where a strategy-proof rule is second-best efficient if in the class of all strategy-proof rules, there is no other strategy-proof rule that gives a “better” outcome than the considered rule in terms of Pareto domination for all preference profiles. We show that in an n person and m good setup for any strategy-proof rule, there exists a second-best efficient rule that Pareto dominates the former. In ∗This paper is based on Anno (2008a,b) and Sasaki (2003), but some additional results are included in the present version. We would like to thank Takashi Akahoshi, Matthew Jackson, Yoichi Kasajima, Kohei Kawamura, Manipushpak Mitra, Shuhei Morimoto, Hervé Moulin, Clemens Puppe, Toyotaka Sakai, Ken Sawada, Tadashi Sekiguchi, Shigehiro Serizawa, Koichi Tadenuma, William Thomson, Takuma Wakayama, Nobuya Watanabe, and Naoki Yoshihara for the helpful comments and discussions. Sasaki’s research is supported by the Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research (No.19530162). †e-mail: [email protected] ‡e-mail: [email protected]