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

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  • Sasaki, Hiroo

    (Rice U and Waseda U)

Abstract

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 preferences 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 strategy-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.

Suggested Citation

  • Sasaki, Hiroo, 2003. "Limitation of Efficiency: Strategy-Proofness and Single-Peaked Preferences with Many Commodities," Working Papers 2003-01, Rice University, Department of Economics.
    • Handle: RePEc:ecl:riceco:2003-01
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    File URL: http://www.ruf.rice.edu/~econ/papers/2003papers/01Sasaki.pdf
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    References listed on IDEAS

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    1. Miki Kato & Shinji Ohseto, 2002. "Toward general impossibility theorems in pure exchange economies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 659-664.
    2. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
    3. Shinji Ohseto, 2000. "Strategy-proof and efficient allocation of an indivisible good on finitely restricted preference domains," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(3), pages 365-374.
    4. Lin Zhou, 1990. "Inefficiency of Strategy-Proof Allocation Mechanisms in Pure Exchange Economies," Cowles Foundation Discussion Papers 954, Cowles Foundation for Research in Economics, Yale University.
    5. Serizawa, Shigehiro & Weymark, John A., 2003. "Efficient strategy-proof exchange and minimum consumption guarantees," Journal of Economic Theory, Elsevier, vol. 109(2), pages 246-263, April.
    6. Pablo Amorós, 2002. "Single-peaked preferences with several commodities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(1), pages 57-67.
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    Cited by:

    1. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506, Elsevier.
    2. Adachi, Tsuyoshi, 2010. "The uniform rule with several commodities: A generalization of Sprumont's characterization," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 952-964, November.
    3. Hidekazu Anno & Hiroo Sasaki, 2013. "Second-best efficiency of allocation rules: strategy-proofness and single-peaked preferences with multiple commodities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 693-716, November.
    4. Anno, Hidekazu & Kurino, Morimitsu, 2016. "On the operation of multiple matching markets," Games and Economic Behavior, Elsevier, vol. 100(C), pages 166-185.
    5. Shuhei Morimoto & Shigehiro Serizawa & Stephen Ching, 2013. "A characterization of the uniform rule with several commodities and agents," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 871-911, March.

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