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Sharing the cost of a network: core and core allocations

Author

Listed:
  • S. H. Tijs

    (CentER and Department of Econometrics, Tilburg University, Tilburg, The Netherlands Final version November 2001)

  • M. Koster

    (Faculty of Economics and Econometrics, Department of Quantitative Economics, University of Amsterdam, The Netherlands)

  • E. Molina

    (Centro de Investigación Operativa, Universidad Miguel Hernández de Elche, Elche, Spain)

  • Y. Sprumont

    (C.R.D.E. et Département de sciences économiques, Université de Montréal, Montréal, Canada)

Abstract

This paper discusses the core of the game corresponding to the standard fixed tree problem. We consider the weighted adaptation of the constrained egalitarian solution of Dutta and Ray (1989). The core of the standard fixed tree game equals the set of all weighted constrained egalitarian solutions. Each weighted constrained egalitarian solution is determined (in polynomial time) as a home-down allocation, which creates further insight in the local behaviour of the weighted constrained egalitarian solution. The constrained egalitarian solution is characterized in terms of a cost sharing mechanism.

Suggested Citation

  • S. H. Tijs & M. Koster & E. Molina & Y. Sprumont, 2002. "Sharing the cost of a network: core and core allocations," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 567-599.
    • Handle: RePEc:spr:jogath:v:30:y:2002:i:4:p:567-599
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    Citations

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    Cited by:

    1. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    2. Koster, M.A.L., 1999. "Weighted Constrained Egalitarianism in TU-Games," Other publications TiSEM 783f5a2d-0367-4dd9-b4d6-a, Tilburg University, School of Economics and Management.
    3. Panova, Elena, 2023. "Sharing cost of network among users with differentiated willingness to pay," Games and Economic Behavior, Elsevier, vol. 142(C), pages 666-689.
    4. Moulin, Herve & Laigret, Francois, 2011. "Equal-need sharing of a network under connectivity constraints," Games and Economic Behavior, Elsevier, vol. 72(1), pages 314-320, May.
    5. Koster, M.A.L., 1999. "Weighted Constrained Egalitarianism in TU-Games," Discussion Paper 1999-107, Tilburg University, Center for Economic Research.
    6. Elena Panova, 2023. "Sharing cost of network among users with differentiated willingness to pay," Post-Print hal-04556220, HAL.
    7. Miquel, S. & van Velzen, S. & Hamers, H.J.M. & Norde, H.W., 2003. "Fixed Tree Games with Repeated Players," Discussion Paper 2003-87, Tilburg University, Center for Economic Research.
    8. Márkus, Judit & Pintér, Miklós & Radványi, Anna, 2011. "The Shapley value for airport and irrigation games," MPRA Paper 30031, University Library of Munich, Germany.
    9. Miquel, S. & van Velzen, S. & Hamers, H.J.M. & Norde, H.W., 2003. "Fixed Tree Games with Repeated Players," Other publications TiSEM 55d10eab-2d36-406b-8e15-4, Tilburg University, School of Economics and Management.
    10. Koster, Maurice, 2002. "Hierarchical constrained egalitarianism in TU-games," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 251-265, March.
    11. Thomson, William, 2024. "Cost allocation and airport problems," Mathematical Social Sciences, Elsevier, vol. 131(C), pages 17-31.
    12. Julio R. Fernández & Inés Gallego & Andrés Jiménez-Losada & Manuel Ordóñez, 2022. "Cost-allocation problems for fuzzy agents in a fixed-tree network," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 531-551, December.
    13. Debing Ni & Yuntong Wang, 2013. "Additive cost sharing on a tree," Working Papers 1307, University of Windsor, Department of Economics.
    14. Bergantiños, G. & Gómez-Rúa, M. & Llorca, N. & Pulido, M. & Sánchez-Soriano, J., 2014. "A new rule for source connection problems," European Journal of Operational Research, Elsevier, vol. 234(3), pages 780-788.
    15. Panova, Elena, 2022. "Sharing cost of network among users with differentiated willingness to pay," TSE Working Papers 22-1356, Toulouse School of Economics (TSE), revised Mar 2023.

    More about this item

    Keywords

    Cooperative game theory · cost sharing · tree games · core · constrained egalitarianism.;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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