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Minimum Cost Spanning Tree Games with Revenues: “Stable” Payoffs when the Core is Empty

Author

Listed:
  • Subiza, Begoña

    (Universitat d’Alacant, MQiTE and IUDESP.)

  • Jiménez-Gómez, José Manuel

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

  • Peris, Josep E

    (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. Estévez-Fernández and Reijnierse (2014) study minimum cost spanning tree problems with revenues (agents can obtain a benefit, if they are connected to the source) and show that the cost-revenues game may have an empty core. In this context, we provide a non-empty unique set that coincides with the core, whenever the core is not empty. In so doing, we define a dominance relation among individually rational distributions of the net revenue and compute the von Neumann-Morgenstern stable set regarding this dominance relation. It is important to highlight that the dominance relation is based on the fact that a majority of agents do not block the sharing of the net revenue.

Suggested Citation

  • 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.
    • Handle: RePEc:ris:qmetal:2024_005
    as

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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Minimum cost spanning tree; Cost-revenues game; Core; Stable set;
    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
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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