, Volume 3, Issue 1–2, pp 29–57 | Cite as

The division problem with maximal capacity constraints

  • Gustavo Bergantiños
  • Jordi Massó
  • Alejandro Neme
Open Access
Original Article


The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. Most of the literature has implicitly assumed that all divisions are feasible. In this paper we consider the division problem when each agent has a maximal capacity due to an objective and verifiable feasibility constraint which imposes an upper bound on his share. Then each agent has a feasible interval of shares where his preferences are single-peaked. A rule has to propose to each agent a feasible share. We focus mainly on strategy-proof, efficient and consistent rules and provide alternative characterizations of the extension of the uniform rule that deals explicitly with agents’ maximal capacity constraints.


Division problem Single-peaked preferences Uniform rule Capacity constraints 

JEL Classification



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Copyright information

© The Author(s) 2011

This article is published under license to BioMed Central Ltd. Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Gustavo Bergantiños
    • 1
  • Jordi Massó
    • 2
  • Alejandro Neme
    • 3
  1. 1.Research Group in Economic Analysis, Facultade de EconómicasUniversidade de VigoVigo (Pontevedra)Spain
  2. 2.Departament d’Economia i d’Història Econòmica and CODEUniversitat Autònoma de BarcelonaBellaterra (Barcelona)Spain
  3. 3.Instituto de Matemática Aplicada San LuisUniversidad Nacional de San Luis and CONICETSan LuisArgentina

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