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The folk rule through a painting procedure for minimum cost spanning tree problems with multiple sources

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  • Bergantiños, Gustavo
  • Navarro, Adriana

Abstract

We consider minimum cost spanning tree problems with multiple sources. We propose a cost allocation rule based on a painting procedure. Agents paint the edges on the paths connecting them to the sources. We prove that the painting rule coincides with the folk rule. Finally, we provide an axiomatic characterization.

Suggested Citation

  • Bergantiños, Gustavo & Navarro, Adriana, 2019. "The folk rule through a painting procedure for minimum cost spanning tree problems with multiple sources," MPRA Paper 91723, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:91723
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    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. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Rosenthal, Edward C., 1987. "The minimum cost spanning forest game," Economics Letters, Elsevier, vol. 23(4), pages 355-357.
    11. 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.
    12. 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 & Vidal-Puga, Juan, 2020. "Cooperative games for minimum cost spanning tree problems," MPRA Paper 104911, University Library of Munich, Germany.
    3. 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.
    4. Hougaard, Jens Leth & Tvede, Mich, 2022. "Trouble comes in threes: Core stability in minimum cost connection networks," European Journal of Operational Research, Elsevier, vol. 297(1), pages 319-324.

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    More about this item

    Keywords

    }minimum cost spanning tree problems with multiple sources; painting rule; axiomatic characterization.;
    All these keywords.

    JEL classification:

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

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