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Cost sharing solutions defined by non-negative eigenvectors

Author

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  • Subiza, Begoña
  • Silva-Reus, José A.
  • Peris, Josep E.

Abstract

The problem of sharing a cost M among n individuals, identified by some characteristic ci∈R+, appears in many real situations. Two important proposals on how to share the cost are the egalitarian and the proportional solutions. In different situations a combination of both distributions provides an interesting approach to the cost sharing problem. In this paper we obtain a family of (compromise) solutions associated to the Perron’s eigenvectors of Levinger’s transformations of a characteristics matrix A. This family includes both the egalitarian and proportional solutions, as well as a set of suitable intermediate proposals, which we analyze in some specific contexts, as claims problems and inventory cost games.

Suggested Citation

  • Subiza, Begoña & Silva-Reus, José A. & Peris, Josep E., 2015. "Cost sharing solutions defined by non-negative eigenvectors," European Journal of Operational Research, Elsevier, vol. 244(2), pages 592-600.
    • Handle: RePEc:eee:ejores:v:244:y:2015:i:2:p:592-600
    DOI: 10.1016/j.ejor.2015.01.055
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    References listed on IDEAS

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    1. Meca, Ana & Timmer, Judith & Garcia-Jurado, Ignacio & Borm, Peter, 2004. "Inventory games," European Journal of Operational Research, Elsevier, vol. 156(1), pages 127-139, July.
      • Meca-Martinez, A. & Timmer, J.B. & Garcia-Jurado, I. & Borm, P.E.M., 1999. "Inventory Games," Other publications TiSEM 21f26b3f-7fae-4f19-908f-a, Tilburg University, School of Economics and Management.
      • Meca, A. & Timmer, J.B. & Garcia-Jurado, I. & Borm, P.E.M., 2004. "Inventory games," Other publications TiSEM 49368f2d-02fc-49c9-9d74-8, Tilburg University, School of Economics and Management.
      • Meca-Martinez, A. & Timmer, J.B. & Garcia-Jurado, I. & Borm, P.E.M., 1999. "Inventory Games," Discussion Paper 1999-53, Tilburg University, Center for Economic Research.
    2. Turkensteen, Marcel & Klose, Andreas, 2012. "Demand dispersion and logistics costs in one-to-many distribution systems," European Journal of Operational Research, Elsevier, vol. 223(2), pages 499-507.
    3. Fiestras-Janeiro, M.G. & García-Jurado, I. & Meca, A. & Mosquera, M.A., 2011. "Cooperative game theory and inventory management," European Journal of Operational Research, Elsevier, vol. 210(3), pages 459-466, May.
    4. Peris, Josep E. & Jiménez-Gómez, José M., 2012. "A Proportional Approach to Bankruptcy Problems with a guaranteed minimum," QM&ET Working Papers 12-7, University of Alicante, D. Quantitative Methods and Economic Theory.
    5. 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.
    6. Karsten, Frank & Basten, Rob J.I., 2014. "Pooling of spare parts between multiple users: How to share the benefits?," European Journal of Operational Research, Elsevier, vol. 233(1), pages 94-104.
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    1. José-Manuel Giménez-Gómez & Josep E. Peris & María-José Solís-Baltodano, 2023. "Resource allocations with guaranteed awards in claims problems," Review of Economic Design, Springer;Society for Economic Design, vol. 27(3), pages 581-602, September.

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    More about this item

    Keywords

    Cost sharing; Egalitarian; Proportional; Perron’s eigenvector; Compromise solution;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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