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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. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, April.
    2. 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.
    3. 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.
    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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