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Minimum cost spanning extension problems : The proportional rule and the decentralized rule

Author

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  • Feltkamp, V.
  • Tijs, S.H.

    (Tilburg University, Center For Economic Research)

  • Muto, S.

Abstract

Minimum cost spanning extension problems are generalizations of minimum cost spanning tree problems (see Bird 1976) where an existing network has to be extended to connect users to a source. In this paper, we present two cost allocation rules for these problems, viz. the proportional rule and the decentralized rule. We introduce algorithms that generate these rules and prove that both rules are refinements of the irreducible core, as defined in Feltkamp, Tijs and Muto (1994b). We then proceed to axiomatically characterize the proportional rule.

Suggested Citation

  • Feltkamp, V. & Tijs, S.H. & Muto, S., 1994. "Minimum cost spanning extension problems : The proportional rule and the decentralized rule," Discussion Paper 1994-96, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:2c6cd46b-7e72-4262-a479-3a5386c90548
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    References listed on IDEAS

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    1. Kuipers, Jeroen, 1993. "On the Core of Information Graph Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 339-350.
    2. Feltkamp, V. & Tijs, S.H. & Muto, S., 1994. "Bird's tree allocations revisited," Discussion Paper 1994-35, Tilburg University, Center for Economic Research.
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    Cited by:

    1. Gerichhausen, Marloes & Hamers, Herbert, 2009. "Partitioning sequencing situations and games," European Journal of Operational Research, Elsevier, vol. 196(1), pages 207-216, July.
    2. Feltkamp, V. & Tijs, S.H. & Muto, S., 1994. "On the irreducible core and the equal remaining obligations rule of minimum cost spanning extension problems," Discussion Paper 1994-106, Tilburg University, Center for Economic Research.
    3. 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.
    4. Stefano Moretti & Stef Tijs & Rodica Branzei & Henk Norde, 2009. "Cost allocation protocols for supply contract design in network situations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 181-202, March.
    5. Gerichhausen, M. & Hamers, H.J.M., 2007. "Partitioning Sequencing Situations and Games," Discussion Paper 2007-40, Tilburg University, Center for Economic Research.
    6. Tijs, Stef & Branzei, Rodica & Moretti, Stefano & Norde, Henk, 2006. "Obligation rules for minimum cost spanning tree situations and their monotonicity properties," European Journal of Operational Research, Elsevier, vol. 175(1), pages 121-134, November.
    7. Norde, H.W., 2013. "The Degree and Cost Adjusted Folk Solution for Minimum Cost Spanning Tree Games," Discussion Paper 2013-039, Tilburg University, Center for Economic Research.
    8. Juan J. Vidal-Puga & Gustavo Bergantiños, 2004. "Defining Rules in Cost Spanning Tree Problems Through the Canonical Form," Working Papers 2004.97, Fondazione Eni Enrico Mattei.
    9. Ciftci, B.B. & Tijs, S.H., 2007. "A Vertex Oriented Approach to Minimum Cost Spanning Tree Problems," Discussion Paper 2007-89, Tilburg University, Center for Economic Research.

    More about this item

    Keywords

    Networks; Cost Allocation; costs and cost price;

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