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A Characterization of the Uniform Rule with Several Commodities and Agents

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  • Shuhei Morimoto
  • Shigehiro Serizawa
  • Stephen Ching

Abstract

We consider the problem of allocating infinitely divisible commodities among a group of agents. Especially, we focus on the case where there are several commodities to be allocated, and agents have continuous, strictly convex, and separable preferences. In this paper, we establish that the uniform rule is the only rule satisfying strategy-proofness, unanimity, symmetry, and nonbossiness.

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File URL: http://www.iser.osaka-u.ac.jp/library/dp/2010/DP0769.pdf
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Bibliographic Info

Paper provided by Institute of Social and Economic Research, Osaka University in its series ISER Discussion Paper with number 0769.

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Date of creation: Aug 2009
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Handle: RePEc:dpr:wpaper:0769

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  1. Maskin, Eric, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 23-38, January.
  2. Hideyuki Mizobuchi & Shigehiro Serizawa, 2005. "Maximal Domain for Strategy-Proof Rules in Allotment Economies," ISER Discussion Paper 0628, Institute of Social and Economic Research, Osaka University.
  3. Satterthwaite, Mark A & Sonnenschein, Hugo, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," Review of Economic Studies, Wiley Blackwell, vol. 48(4), pages 587-97, October.
  4. Barbera, S. & Gul, F. & Stacchetti, E., 1992. "Generalized Median Voter Schemes and Committees," UFAE and IAE Working Papers 184.92, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  5. Michel Breton & Vera Zaporozhets, 2009. "On the equivalence of coalitional and individual strategy-proofness properties," Social Choice and Welfare, Springer, vol. 33(2), pages 287-309, August.
  6. Bogomolnaia, Anna & Deb, Rajat & Ehlers, Lars, 2005. "Strategy-proof assignment on the full preference domain," Journal of Economic Theory, Elsevier, vol. 123(2), pages 161-186, August.
  7. Barbera, S. & Masso, J. & Serizawa, S., 1998. "Strategy-Proof Voting on Compact Ranges," Games and Economic Behavior, Elsevier, vol. 25(2), pages 272-291, November.
  8. Lars Ehlers & Bettina Klaus, 2003. "Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems," Social Choice and Welfare, Springer, vol. 21(2), pages 265-280, October.
  9. Miyagawa, Eiichi, 2001. "House Allocation with Transfers," Journal of Economic Theory, Elsevier, vol. 100(2), pages 329-355, October.
  10. Volij, Oscar & Otten, Gert-Jan & Peters, Hans, 1996. "Two Characterizations of the Uniform Rule for Division Problems with Single-Peaked Preferences," Staff General Research Papers 5108, Iowa State University, Department of Economics.
  11. Barbera, Salvador & Jackson, Matthew O, 1995. "Strategy-Proof Exchange," Econometrica, Econometric Society, vol. 63(1), pages 51-87, January.
  12. Border, Kim C & Jordan, J S, 1983. "Straightforward Elections, Unanimity and Phantom Voters," Review of Economic Studies, Wiley Blackwell, vol. 50(1), pages 153-70, January.
  13. Thomson, William, 1997. "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 76(1), pages 145-168, September.
  14. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2009. "Individual versus group strategy proofedness: when do they coincide?," Working Papers 372, Barcelona Graduate School of Economics.
  15. Shigehiro Serizawa, 1997. "Strategy-proof and individually rational social choice functions for public good economies," Economic Theory, Springer, vol. 9(2), pages 379-380.
  16. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
  17. Ching, Stephen & Serizawa, Shigehiro, 1998. "A Maximal Domain for the Existence of Strategy-Proof Rules," Journal of Economic Theory, Elsevier, vol. 78(1), pages 157-166, January.
  18. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
  19. Schummer, James, 2000. "Eliciting Preferences to Assign Positions and Compensation," Games and Economic Behavior, Elsevier, vol. 30(2), pages 293-318, February.
  20. Shigehiro Serizawa, 2006. "Pairwise Strategy-Proofness and Self-Enforcing Manipulation," Social Choice and Welfare, Springer, vol. 26(2), pages 305-331, April.
  21. Thomson William, 1994. "Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Journal of Economic Theory, Elsevier, vol. 63(2), pages 219-245, August.
  22. Svensson, Lars-Gunnar & Larsson, Bo, 2000. "Strategy-Proof and Nonbossy Allocation of Indivisible Goods and Money," Working Papers 2000:11, Lund University, Department of Economics.
  23. 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.
  24. William Thomson, 2010. "Implementation of solutions to the problem of fair division when preferences are single-peaked," Review of Economic Design, Springer, vol. 14(1), pages 1-15, March.
  25. Thomson, William, 1995. "Population-Monotonic Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Economic Theory, Springer, vol. 5(2), pages 229-46, March.
  26. John Hatfield, 2009. "Strategy-proof, efficient, and nonbossy quota allocations," Social Choice and Welfare, Springer, vol. 33(3), pages 505-515, September.
  27. M. Fleurbaey & F. Maniquet, 1997. "Implementability and Horizontal Equity Imply No-Envy," Econometrica, Econometric Society, vol. 65(5), pages 1215-1220, September.
  28. Serizawa, Shigehiro, 2002. "Inefficiency of Strategy-Proof Rules for Pure Exchange Economies," Journal of Economic Theory, Elsevier, vol. 106(2), pages 219-241, October.
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Cited by:
  1. 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.
  2. Erlanson, Albin & Szwagrzak, Karol, 2013. "Strategy-Proof Package Assignment," Working Papers 2013:43, Lund University, Department of Economics.

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