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A monotonic and merge-proof rule in minimum cost spanning tree situations

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  • María Gómez-Rúa

    (Universidade de Vigo)

  • Juan Vidal-Puga

    (Universidade de Vigo)

Abstract

We present a new model for cost sharing in minimum cost spanning tree problems to allow planners to identify how many agents merge. Under this new framework, in contrast to the traditional model, there are rules that satisfy the property of Merge-proofness. Furthermore, strengthening this property and adding some others, such as Population Monotonicity and Solidarity, makes it possible to define a unique rule that coincides with the weighted Shapley value of an associated cost game.

Suggested Citation

  • María Gómez-Rúa & Juan Vidal-Puga, 2017. "A monotonic and merge-proof rule in minimum cost spanning tree situations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 813-826, March.
    • Handle: RePEc:spr:joecth:v:63:y:2017:i:3:d:10.1007_s00199-016-0996-x
    DOI: 10.1007/s00199-016-0996-x
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    Cited by:

    1. Bergantiños, Gustavo & Vidal-Puga, Juan, 2020. "Cooperative games for minimum cost spanning tree problems," MPRA Paper 104911, University Library of Munich, Germany.
    2. Liu, Siwen & Borm, Peter & Norde, Henk, 2023. "Induced Rules for Minimum Cost Spanning Tree Problems : towards Merge-proofness and Coalitional Stability," Discussion Paper 2023-021, Tilburg University, Center for Economic Research.
    3. Liu, Siwen & Borm, Peter & Norde, Henk, 2023. "Induced Rules for Minimum Cost Spanning Tree Problems : towards Merge-proofness and Coalitional Stability," Other publications TiSEM bf366633-5301-4aad-81c8-a, Tilburg University, School of Economics and Management.
    4. 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.
    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. 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.
    7. Ruben Juarez & Kohei Nitta & Miguel Vargas, 2020. "Profit-sharing and efficient time allocation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 817-846, October.

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    More about this item

    Keywords

    Minimum cost spanning tree problems; Cost sharing; Core Selection; Cost Monotonicity; Merge-proofness; Weighted Shapley value;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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