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On Some Properties of Cost Allocation Rules in Minimum Cost Spanning Tree Problems

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Abstract

We consider four cost allocation rules in minimum cost spanning tree problems. These rules were introduced by Bird (1976), Dutta and Kar (2004), Kar (2002), and Feltkamp, Tijs and Muto (1994), respectively. We give a list of desirable properties and we study which properties are satisfied by these rules.

Suggested Citation

  • 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.
    • Handle: RePEc:fau:aucocz:au2008_251
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    1. Gustavo Bergantiños & Leticia Lorenzo, 2004. "A non-cooperative approach to the cost spanning tree problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(3), pages 393-403, 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. 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.
    4. 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.
    5. 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.
    6. Kar, Anirban, 2002. "Axiomatization of the Shapley Value on Minimum Cost Spanning Tree Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 265-277, February.
    7. 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.
    8. Gustavo Bergantiños & Juan Vidal-Puga, 2007. "The optimistic TU game in minimum cost spanning tree problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 223-239, October.
    9. Gustavo Bergantiños & Juan Vidal-Puga, 2004. "Additivity in cost spanning tree problems," Game Theory and Information 0405001, University Library of Munich, Germany.
    10. Gustavo Bergantiños & Leticia Lorenzo, 2005. "Optimal Equilibria in the Non-Cooperative Game Associated with Cost Spanning Tree Problems," Annals of Operations Research, Springer, vol. 137(1), pages 101-115, July.
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    Cited by:

    1. Gustavo Bergantiños & Youngsub Chun & Eunju Lee & Leticia Lorenzo, 2022. "The Folk Rule for Minimum Cost Spanning Tree Problems with Multiple Sources," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 24(01), pages 1-36, March.
    2. Subiza, Begoña & Giménez, José Manuel & Peris, Josep E., 2015. "Folk solution for simple minimum cost spanning tree problems," QM&ET Working Papers 15-7, University of Alicante, D. Quantitative Methods and Economic Theory.
    3. José-Manuel Giménez-Gómez & Josep E Peris & Begoña Subiza, 2020. "An egalitarian approach for sharing the cost of a spanning tree," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-14, July.
    4. Trudeau, Christian, 2012. "A new stable and more responsive cost sharing solution for minimum cost spanning tree problems," Games and Economic Behavior, Elsevier, vol. 75(1), pages 402-412.
    5. María Gómez-Rúa & Juan Vidal-Puga, 2017. "A monotonic and merge-proof rule in minimum cost spanning tree situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 813-826, March.
    6. Giménez-Gómez, José M. & Peris, Josep E. & Subiza, Begoña, 2016. "A `Solidarity' Approach to the Problem of Sharing a Network Cost," QM&ET Working Papers 16-5, University of Alicante, D. Quantitative Methods and Economic Theory.
    7. Hernández, Penélope & Peris, Josep E. & Vidal-Puga, Juan, 2023. "A non-cooperative approach to the folk rule in minimum cost spanning tree problems," European Journal of Operational Research, Elsevier, vol. 307(2), pages 922-928.

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    More about this item

    Keywords

    Minimum cost spanning tree; properties;

    JEL classification:

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

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