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Reallocation of an infinitely divisible good

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  • Bettina Klaus

    (Department of Quantitative Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, THE NETHERLANDS)

  • Hans Peters

    (Department of Quantitative Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, THE NETHERLANDS)

  • Ton Storcken

    (Department of Quantitative Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, THE NETHERLANDS)

Abstract

We consider the problem of reallocating the total initial endowments of an infinitely divisible commodity among agents with single-peaked preferences. With the uniform reallocation rule we propose a solution which satisfies many appealing properties, describing the effect of population and endowment variations on the outcome. The central properties which are studied in this context are population monotonicity, bilateral consistency, (endowment) monotonicity and (endowment) strategy-proofness. Furthermore, the uniform reallocation rule is Pareto optimal and satisfies several equity conditions, e.g., equal-treatment and envy-freeness. We study the trade-off between properties concerning variation and properties concerning equity. Furthermore, we provide several characterizations of the uniform reallocation rule based on these properties.

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 10 (1997)
Issue (Month): 2 ()
Pages: 305-333

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Handle: RePEc:spr:joecth:v:10:y:1997:i:2:p:305-333

Note: Received: August 29, 1995; revised version June 26, 1996
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References

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  1. 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.
  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 509-19, March.
  3. Klaus,Bettina & Peters,Hans & Storcken,Ton, 1995. "Strategy-proof division with single-peaked preferences and initial endowments," Research Memorandum 001, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  4. 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.
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Cited by:
  1. Erik Ansink & Hans-Peter Weikard, 2009. "Sequential Sharing Rules for River Sharing Problems," Working Papers 2009.114, Fondazione Eni Enrico Mattei.
  2. 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.
  3. Murat Atlamaz & Bettina Klaus, 2003. "Manipulation via Endowments in Exchange Markets with Indivisible Goods," UFAE and IAE Working Papers 598.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  4. Özgür Kıbrıs & Serkan Küçükşenel, 2009. "Uniform trade rules for uncleared markets," Social Choice and Welfare, Springer, vol. 32(1), pages 101-121, January.
  5. Erik Ansink & Carmen Marchiori, 2009. "Reallocating Water: An Application of Sequent," Working Papers 2009.126, Fondazione Eni Enrico Mattei.
  6. Ehlers, Lars, 2003. "Multiple public goods, lexicographic preferences, and single-plateaued preference rules," Games and Economic Behavior, Elsevier, vol. 43(1), pages 1-27, April.
  7. Rahmi Ilkilic, 2012. "Allocation rules on networks," DOCUMENTOS DE TRABAJO 009380, UNIVERSIDAD DEL ROSARIO.
  8. Özgür Kýbrýs & Serkan Küçükþenel, 2005. "Trade rules for uncleared markets," Microeconomics 0508002, EconWPA.
  9. Moreno, Bernardo, 2002. "Single-peaked preferences, endowments and population-monotonicity," Economics Letters, Elsevier, vol. 75(1), pages 87-95, March.

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