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Sequential contributions rules for minimum cost spanning tree problems

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  • Chun, Youngsub
  • Lee, Joosung

Abstract

We introduce a family of sequential contributions rules for minimum cost spanning tree problems. Each member of the family assigns an agent part of the cost of connecting him to his immediate predecessor, and all of his followers are equally responsible for the remaining part. We characterize the family by imposing the axioms of efficiency, non-negativity, independence of following costs, group independence, and weak first-link consistency. The Bird and the sequential equal contributions rules are two distinguished members of the family. The Bird rule is obtained by requiring an agent to pay the entire cost of connecting him to his immediate predecessor, and the sequential equal contributions rule is obtained by requiring an agent and each of his followers to be equally responsible for this cost. We show how each of these two rules can be singled out from the family.

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  • Chun, Youngsub & Lee, Joosung, 2012. "Sequential contributions rules for minimum cost spanning tree problems," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 136-143.
    • Handle: RePEc:eee:matsoc:v:64:y:2012:i:2:p:136-143
    DOI: 10.1016/j.mathsocsci.2012.02.001
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    Cited by:

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    2. Wenzhong Li & Genjiu Xu & René van den Brink, 2023. "Two new classes of methods to share the cost of cleaning up a polluted river," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(1), pages 35-59, July.
    3. 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.
    4. Bergantiños, Gustavo & Vidal-Puga, Juan, 2020. "Cooperative games for minimum cost spanning tree problems," MPRA Paper 104911, University Library of Munich, Germany.
    5. Changyong Han & Bawoo Kim & Youngsub Chun, 2024. "Demand operators and the Dutta–Kar rule for minimum cost spanning tree problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(1), pages 101-124, August.
    6. Gustavo Bergantiños & Juan Vidal-Puga, 2021. "A review of cooperative rules and their associated algorithms for minimum-cost spanning tree problems," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 73-100, March.

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