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Cost sharing solutions de fined by non-negative eigenvectors

  • Subiza, Begoña

    ()

    (Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica)

  • Silva-Reus, José Ángel

    ()

    (Instituto Interuniversitario de Desarrollo Social y Paz)

  • Peris, Josep E.

    ()

    (Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica)

We consider a cost sharing problem, where each individual is identi ed by a characteristic (a positive real number) ci: The two main positions on how to share a common cost M are the Egalitarian and the Proportional solutions. These solutions can be obtained as the Perron's eigenvectors (right and left, respectively) of a characteristics matrix A, with rk(A) = 1; de fined from the individuals' characteristics ci: Then, the right Perron's eigenvector associated to any Levinger's transformation L(α) = α A'+(1-α )A; α є [0;1] ; provides a dif ferent solution to the cost sharing problem (from the egalitarian one, for α = 0; to the proportional one, for α = 1). We are interested in analyzing the properties of the components of these Perron's eigenvectors as (non linear) functions of the parameter α that de fines the convex combination of matrices A and A': These components de fine the solution of the cost sharing problem, that could be understood as a compromise between the egalitarian and proportional approaches. We prove that when the associated positive eigenvector is normalized, its components have a monotone behaviour in the unit interval [0;1]: Additional properties and a way of selecting a particular compromise solution are provided.

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Paper provided by Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica in its series QM&ET Working Papers with number 13-6.

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Length: 21 pages
Date of creation: 10 Dec 2013
Date of revision:
Handle: RePEc:ris:qmetal:2013_006
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  1. José M. Jiménez Gómez & Josep Enric Peris Ferrando, 2012. "A proportional approach to bankruptcy. Problems with a guaranteed minimum," Working Papers. Serie AD 2012-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  2. Giménez-Gómez, José-Manuel & Peris, Josep E., 2014. "A proportional approach to claims problems with a guaranteed minimum," European Journal of Operational Research, Elsevier, vol. 232(1), pages 109-116.
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