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On the set of extreme core allocations for minimal cost spanning tree problems

Author

Listed:
  • Christian Trudeau

    (Department of Economics, University of Windsor)

  • Juan Vidal-Puga

    (Research Group of Economic Analysis and Departamento de Estatistica e IO, Universidade de Vigo)

Abstract

Minimal cost spanning tree problems connect agents efficiently to a source when agents are located at different points and the cost of using an edge is fixed. We propose a method, based on the concept of marginal games, to generate all extreme points of the corresponding core. We show that three of the most famous solutions to share the cost of mcst problems, the Bird, folk and cycle-complete solutions, are closely related to our method.

Suggested Citation

  • Christian Trudeau & Juan Vidal-Puga, 2015. "On the set of extreme core allocations for minimal cost spanning tree problems," Working Papers 1505, University of Windsor, Department of Economics.
    • Handle: RePEc:wis:wpaper:1505
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    References listed on IDEAS

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    Cited by:

    1. Christian Trudeau, 2023. "Minimum cost spanning tree problems as value sharing problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 253-272, March.
    2. 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.
    3. G. Bergantiños & J. Vidal-Puga, 2020. "One-way and two-way cost allocation in hub network problems," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(1), pages 199-234, March.
    4. Grabisch, Michel & Sudhölter, Peter, 2018. "On a class of vertices of the core," Games and Economic Behavior, Elsevier, vol. 108(C), pages 541-557.
    5. Bergantiños, Gustavo & Vidal-Puga, Juan, 2020. "Cooperative games for minimum cost spanning tree problems," MPRA Paper 104911, University Library of Munich, Germany.
    6. Trudeau, Christian & Vidal-Puga, Juan, 2020. "Clique games: A family of games with coincidence between the nucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 8-14.
    7. Marina Núñez, 2016. "Comments on: Remarkable polyhedra related to set functions, games and capacities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 327-329, July.
    8. M. A. Hinojosa & A. Caro, 2021. "A non-cooperative game theory approach to cost sharing in networks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(2), pages 219-251, October.
    9. Bahel, Eric & Trudeau, Christian, 2019. "A cost sharing example in which subsidies are necessary for stability," Economics Letters, Elsevier, vol. 185(C).
    10. Bahel, Eric, 2021. "Hyperadditive games and applications to networks or matching problems," Journal of Economic Theory, Elsevier, vol. 191(C).
    11. 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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    More about this item

    Keywords

    Minimal cost spanning tree problems; extreme core allocations; reduced game; Bird solution; folk solution; cycle-complete solution.;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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