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A review of cooperative rules and their associated algorithms for minimum-cost spanning tree problems

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  • Gustavo Bergantiños

    (Universidade de Vigo)

  • Juan Vidal-Puga

    (Universidade de Vigo)

Abstract

Minimum-cost spanning tree problems are well-known problems in the operations research literature. Some agents, located at different geographical places, want a service provided by a common supplier. Agents will be served through costly connections. Some part of the literature has focused, mainly, in studying how to allocate the connection cost among the agents. We review the papers that have addressed the allocation problem using cooperative game theory. We also relate the rules defined through cooperative games with rules defined directly from the problem, either through algorithms for computing a minimal tree, either through a cone-wise decomposition.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:series:v:12:y:2021:i:1:d:10.1007_s13209-021-00230-y
    DOI: 10.1007/s13209-021-00230-y
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    Cited by:

    1. Davila-Pena, Laura & Borm, Peter & Garcia-Jurado, Ignacio & Schouten, Jop, 2023. "An Allocation Rule for Graph Machine Scheduling Problems," Other publications TiSEM 17013f33-1d65-4294-802c-b, Tilburg University, School of Economics and Management.
    2. 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.
    3. G. Bergantiños & Juan D. Moreno-Ternero, 2024. "Anonymity in sharing the revenues from broadcasting sports leagues," Annals of Operations Research, Springer, vol. 336(3), pages 1395-1417, May.
    4. Bergantiños, Gustavo & Groba, Carlos & Sartal, Antonio, 2023. "Applying the Shapley value to the tuna fishery," European Journal of Operational Research, Elsevier, vol. 309(1), pages 306-318.
    5. Davila-Pena, Laura & Borm, Peter & Garcia-Jurado, Ignacio & Schouten, Jop, 2023. "An Allocation Rule for Graph Machine Scheduling Problems," Discussion Paper 2023-009, Tilburg University, Center for Economic Research.
    6. Panova, Elena, 2023. "Sharing cost of network among users with differentiated willingness to pay," Games and Economic Behavior, Elsevier, vol. 142(C), pages 666-689.
    7. Subiza, Begoña & Giménez-Gómez, José Manuel & Peris, Josep E., 2024. "Non-Emptiness of the Core of MCST Games with Revenues: a Necessary and Some Sufficient Conditions," QM&ET Working Papers 24-4, University of Alicante, D. Quantitative Methods and Economic Theory.
    8. Subiza, Begoña & Jiménez-Gómez, José Manuel & Peris, Josep E, 2024. "Minimum Cost Spanning Tree Games with Revenues: “Stable” Payoffs when the Core is Empty," QM&ET Working Papers 24-5, University of Alicante, D. Quantitative Methods and Economic Theory.
    9. Elena Panova, 2023. "Sharing cost of network among users with differentiated willingness to pay," Post-Print hal-04556220, HAL.
    10. Panova, Elena, 2022. "Sharing cost of network among users with differentiated willingness to pay," TSE Working Papers 22-1356, Toulouse School of Economics (TSE), revised Mar 2023.

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    More about this item

    Keywords

    Minimum-cost spanning tree problems; Cooperative games; Algorithms; Core; Shapley value;
    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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