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

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  • Gómez-Rúa, María
  • Vidal-Puga, Juan

Abstract

We present a new model for cost sharing in minimum cost spanning tree problems, so that the planner can identify the agents that merge. Under this new framework, and as opposed to the traditional model, there exist rules that satisfy merge-proofness. Besides, by strengthening this property and adding some other properties, such as population-monotonicity and solidarity, we characterize a unique rule that coincides with the weighted Shapley value of an associated cost game.

Suggested Citation

  • Gómez-Rúa, María & Vidal-Puga, Juan, 2015. "A monotonic and merge-proof rule in minimum cost spanning tree situations," MPRA Paper 62923, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:62923
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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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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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