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Non-Emptiness of the Core of MCST Games with Revenues: a Necessary and Some Sufficient Conditions

Author

Listed:
  • Begoña Subiza

    (Universitat d'Alacant, MQiTE and IUDESP)

  • José Manuel Giménez-Gómez

    (Universitat Rovira i Virgili, Dept. d'Economia and ECO-SOS)

  • Josep E. Peris

    (Universitat d'Alacant, MQiTE and IUDESP)

Abstract

A minimum cost spanning tree problem analyzes the way to efficiently connect agents to a source when they are located at different places. Estevez-Fernandez and Reijnierse (2014) investigate minimum cost spanning tree problems with revenues, where agents can obtain benefits if they are connected to the source. They figure out that ensuring the non-emptiness of the core in cost-revenue games presents a significant challenge. We address minimum cost spanning tree problems with revenues, focusing on two main objectives: first, to derive general necessary conditions for the non-emptiness of the core; and second, to identify sufficient conditions, within specific contexts, that guarantee that the core is not empty.

Suggested Citation

  • Begoña Subiza & José Manuel Giménez-Gómez & Josep E. Peris, 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.
    • Handle: RePEc:ris:qmetal:2024_004
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    References listed on IDEAS

    as
    1. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, December.
    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. Estévez-Fernández, Arantza & Reijnierse, Hans, 2014. "On the core of cost-revenue games: Minimum cost spanning tree games with revenues," European Journal of Operational Research, Elsevier, vol. 237(2), pages 606-616.
    5. 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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    Keywords

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    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
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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