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The Folk Rule for Minimum Cost Spanning Tree Problems with Multiple Sources

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  • Bergantiños, Gustavo
  • Chun, Youngsub
  • Lee, Eunju
  • Lorenzo, Leticia

Abstract

We consider a problem where a group of agents is interested in some goods provided by a supplier with multiple sources. To be served, each agent should be connected directly or indirectly to all sources of the supplier for a safety reason. This problem generalizes the classical minimum cost spanning problem with one source by allowing the possibility of multiple sources. In this paper, we extend the definitions of the folk rule to be suitable for minimal cost spanning tree problems with multiple sources and present its axiomatic characterizations.

Suggested Citation

  • Bergantiños, Gustavo & Chun, Youngsub & Lee, Eunju & Lorenzo, Leticia, 2019. "The Folk Rule for Minimum Cost Spanning Tree Problems with Multiple Sources," MPRA Paper 97141, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:97141
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    References listed on IDEAS

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    1. Bergantiños, Gustavo & Lorenzo, Leticia & Lorenzo-Freire, Silvia, 2011. "A generalization of obligation rules for minimum cost spanning tree problems," European Journal of Operational Research, Elsevier, vol. 211(1), pages 122-129, May.
    2. Bergantiños, Gustavo & Kar, Anirban, 2010. "On obligation rules for minimum cost spanning tree problems," Games and Economic Behavior, Elsevier, vol. 69(2), pages 224-237, July.
    3. Gustavo Bergantiños & Silvia Lorenzo-Freire, 2008. "A characterization of optimistic weighted Shapley rules in minimum cost spanning tree problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 523-538, June.
    4. Norde, Henk & Moretti, Stefano & Tijs, Stef, 2004. "Minimum cost spanning tree games and population monotonic allocation schemes," European Journal of Operational Research, Elsevier, vol. 154(1), pages 84-97, April.
    5. Rosenthal, Edward C., 1987. "The minimum cost spanning forest game," Economics Letters, Elsevier, vol. 23(4), pages 355-357.
    6. Dutta, Bhaskar & Kar, Anirban, 2004. "Cost monotonicity, consistency and minimum cost spanning tree games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 223-248, August.
    7. Gouveia, Luis & Leitner, Markus & Ljubić, Ivana, 2014. "Hop constrained Steiner trees with multiple root nodes," European Journal of Operational Research, Elsevier, vol. 236(1), pages 100-112.
    8. 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.
    9. Bergantinos, Gustavo & Vidal-Puga, Juan J., 2007. "A fair rule in minimum cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 326-352, November.
    10. Brânzei, R. & Moretti, S. & Norde, H.W. & Tijs, S.H., 2003. "The P-Value for Cost Sharing in Minimum Cost Spanning Tree Situations," Discussion Paper 2003-129, Tilburg University, Center for Economic Research.
    11. Bergantinos, Gustavo & Lorenzo-Freire, Silvia, 2008. ""Optimistic" weighted Shapley rules in minimum cost spanning tree problems," European Journal of Operational Research, Elsevier, vol. 185(1), pages 289-298, February.
    12. Daniel Granot & Frieda Granot, 1992. "Computational Complexity of a Cost Allocation Approach to a Fixed Cost Spanning Forest Problem," Mathematics of Operations Research, INFORMS, vol. 17(4), pages 765-780, November.
    13. Leticia Lorenzo & Silvia Lorenzo-Freire, 2009. "A characterization of Kruskal sharing rules for minimum cost spanning tree problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 107-126, March.
    14. Bergantiños, Gustavo & Vidal-Puga, Juan, 2009. "Additivity in minimum cost spanning tree problems," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 38-42, January.
    15. Stefano Moretti & Rodica Branzei & Henk Norde & Stef Tijs, 2004. "The P-value for cost sharing in minimum," Theory and Decision, Springer, vol. 56(1), pages 47-61, April.
    16. Gustavo Bergantinos & Juan Vidal-Puga, 2008. "On Some Properties of Cost Allocation Rules in Minimum Cost Spanning Tree Problems," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 2(3), pages 251-267, December.
    17. Gustavo Bergantiños & Juan Vidal-Puga, 2015. "Characterization of monotonic rules in minimum cost spanning tree problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 835-868, November.
    18. Gustavo Bergantiños & Leticia Lorenzo & Silvia Lorenzo-Freire, 2010. "The family of cost monotonic and cost additive rules in minimum cost spanning tree problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(4), pages 695-710, April.
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    Cited by:

    1. Gustavo Bergantiños & Leticia Lorenzo, 2021. "Cost additive rules in minimum cost spanning tree problems with multiple sources," Annals of Operations Research, Springer, vol. 301(1), pages 5-15, June.
    2. Bergantiños, Gustavo & Navarro, Adriana, 2019. "Characterization of the painting rule for multi-source minimal cost spanning tree problems," MPRA Paper 93266, University Library of Munich, Germany.

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    More about this item

    Keywords

    minimum cost spanning tree problems; multiple sources; folk rule; axiomatic characterizations.;
    All these keywords.

    JEL classification:

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

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