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Sharing the cost of maximum quality optimal spanning trees

Author

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  • Begoña Subiza

    (Universitat d’Alacant, Mètodes Quantitatius i Teoria Econòmica (MQiTE) and Institut Interuniversitari Desenvolupament Social i Pau (IUDESP))

  • Josep E. Peris

    (Universitat d’Alacant, Mètodes Quantitatius i Teoria Econòmica (MQiTE) and Institut Interuniversitari Desenvolupament Social i Pau (IUDESP))

Abstract

Minimum cost spanning tree problems have been widely studied in operation research and economic literature. Multi-objective optimal spanning trees provide a more realistic representation of different actual problems. Once an optimal tree is obtained, how to allocate its cost among the agents defines a situation quite different from what we have in the minimum cost spanning tree problems. In this paper, we analyze a multi-objective problem where the goal is to connect a group of agents to a source with the highest possible quality at the cheapest cost. We compute optimal networks and propose cost allocations for the total cost of the project. We analyze properties of the proposed solution; in particular, we focus on coalitional stability (core selection), a central concern in the literature on minimum cost spanning tree problems.

Suggested Citation

  • Begoña Subiza & Josep E. Peris, 2021. "Sharing the cost of maximum quality optimal spanning trees," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 470-493, July.
    • Handle: RePEc:spr:topjnl:v:29:y:2021:i:2:d:10.1007_s11750-020-00568-9
    DOI: 10.1007/s11750-020-00568-9
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    References listed on IDEAS

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    1. Feltkamp, V. & Tijs, S.H. & Muto, S., 1994. "On the irreducible core and the equal remaining obligations rule of minimum cost spanning extension problems," Other publications TiSEM 56ea8c64-a05f-4b3f-ab61-9, Tilburg University, School of Economics and Management.
    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. Christian Trudeau, 2013. "Characterizations Of The Kar And Folk Solutions For Minimum Cost Spanning Tree Problems," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-16.
    4. Christian Trudeau, 2014. "Characterizations of the cycle-complete and folk solutions for minimum cost spanning tree problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 941-957, April.
    5. 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.
    6. Trudeau, Christian, 2012. "A new stable and more responsive cost sharing solution for minimum cost spanning tree problems," Games and Economic Behavior, Elsevier, vol. 75(1), pages 402-412.
    7. Feltkamp, V. & Tijs, S.H. & Muto, S., 1994. "Minimum cost spanning extension problems : The proportional rule and the decentralized rule," Other publications TiSEM 2c6cd46b-7e72-4262-a479-3, Tilburg University, School of Economics and Management.
    8. Kar, Anirban, 2002. "Axiomatization of the Shapley Value on Minimum Cost Spanning Tree Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 265-277, February.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Minimum cost spanning tree; Multi-objective decision making; Quality; Cost sharing;
    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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