IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v78y2024i1d10.1007_s00199-023-01526-9.html
   My bibliography  Save this article

Demand operators and the Dutta–Kar rule for minimum cost spanning tree problems

Author

Listed:
  • Changyong Han

    (Korea SMEs and Startups Institute)

  • Bawoo Kim

    (Samsung Electronics)

  • Youngsub Chun

    (Seoul National University)

Abstract

Granot and Huberman (Math Program 29:323–347, 1984) introduced two demand operators, the weak demand operator and the strong demand operator, for minimum cost spanning tree problems, which are intended to measure the maximum amount that each agent can demand from her followers in compensation for making a link to her. We investigate the implications of these demand operators by introducing a procedure which enables us to sequentially calculate the maximum for each agent. On the irreducible cost matrix, by applying the weak demand operator sequentially to each agent, the Dutta–Kar allocation (Dutta and Kar in Games Econ Behav 48:223–248, 2004) is obtained if the procedure is initiated from any efficient allocation. For the strong demand operator, the Dutta–Kar allocation is obtained if the procedure is initiated from any allocation in the irreducible core.

Suggested Citation

  • Changyong Han & Bawoo Kim & Youngsub Chun, 2024. "Demand operators and the Dutta–Kar rule for minimum cost spanning tree problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(1), pages 101-124, August.
    • Handle: RePEc:spr:joecth:v:78:y:2024:i:1:d:10.1007_s00199-023-01526-9
    DOI: 10.1007/s00199-023-01526-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00199-023-01526-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00199-023-01526-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bergantiños, Gustavo & Lorenzo, Leticia & Lorenzo-Freire, Silvia, 2011. "A generalization of obligation rules for minimum cost spanning tree problems," European Journal of Operational Research, Elsevier, vol. 211(1), pages 122-129, May.
    2. Bergantiños, Gustavo & Kar, Anirban, 2010. "On obligation rules for minimum cost spanning tree problems," Games and Economic Behavior, Elsevier, vol. 69(2), pages 224-237, July.
    3. Chun, Youngsub & Lee, Joosung, 2012. "Sequential contributions rules for minimum cost spanning tree problems," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 136-143.
    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. 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.
    6. Dutta, Bhaskar & Kar, Anirban, 2004. "Cost monotonicity, consistency and minimum cost spanning tree games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 223-248, August.
    7. 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.
    8. Trudeau, Christian & Vidal-Puga, Juan, 2017. "On the set of extreme core allocations for minimal cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 169(C), pages 425-452.
    9. Leticia Lorenzo & Silvia Lorenzo-Freire, 2009. "A characterization of Kruskal sharing rules for minimum cost spanning tree problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 107-126, March.
    10. Bergantiños, Gustavo & Vidal-Puga, Juan, 2010. "Realizing fair outcomes in minimum cost spanning tree problems through non-cooperative mechanisms," European Journal of Operational Research, Elsevier, vol. 201(3), pages 811-820, March.
    11. 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.
    12. 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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bergantiños, Gustavo & Vidal-Puga, Juan, 2020. "Cooperative games for minimum cost spanning tree problems," MPRA Paper 104911, University Library of Munich, Germany.
    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. Gustavo Bergantiños & Juan Vidal-Puga, 2015. "Characterization of monotonic rules in minimum cost spanning tree problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 835-868, November.
    4. Gustavo Bergantiños & Leticia Lorenzo, 2021. "Cost additive rules in minimum cost spanning tree problems with multiple sources," Annals of Operations Research, Springer, vol. 301(1), pages 5-15, June.
    5. Christian Trudeau, 2023. "Minimum cost spanning tree problems as value sharing problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 253-272, March.
    6. 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.
    7. Bergantiños, Gustavo & Martínez, Ricardo, 2014. "Cost allocation in asymmetric trees," European Journal of Operational Research, Elsevier, vol. 237(3), pages 975-987.
    8. Gustavo Bergantiños & Youngsub Chun & Eunju Lee & Leticia Lorenzo, 2022. "The Folk Rule for Minimum Cost Spanning Tree Problems with Multiple Sources," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 24(01), pages 1-36, March.
    9. José-Manuel Giménez-Gómez & Josep E Peris & Begoña Subiza, 2020. "An egalitarian approach for sharing the cost of a spanning tree," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-14, July.
    10. Norde, Henk, 2019. "The degree and cost adjusted folk solution for minimum cost spanning tree games," Games and Economic Behavior, Elsevier, vol. 113(C), pages 734-742.
    11. Norde, H.W., 2013. "The Degree and Cost Adjusted Folk Solution for Minimum Cost Spanning Tree Games," Other publications TiSEM 7ac3a323-f736-46a6-b568-c, Tilburg University, School of Economics and Management.
    12. Norde, H.W., 2013. "The Degree and Cost Adjusted Folk Solution for Minimum Cost Spanning Tree Games," Discussion Paper 2013-039, Tilburg University, Center for Economic Research.
    13. Hernández, Penélope & Peris, Josep E. & Silva-Reus, José A., 2016. "Strategic sharing of a costly network," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 72-82.
    14. Bergantiños, Gustavo & Lorenzo, Leticia & Lorenzo-Freire, Silvia, 2011. "A generalization of obligation rules for minimum cost spanning tree problems," European Journal of Operational Research, Elsevier, vol. 211(1), pages 122-129, May.
    15. Dutta, Bhaskar & Mishra, Debasis, 2012. "Minimum cost arborescences," Games and Economic Behavior, Elsevier, vol. 74(1), pages 120-143.
    16. Gustavo Bergantiños & María Gómez-Rúa, 2015. "An axiomatic approach in minimum cost spanning tree problems with groups," Annals of Operations Research, Springer, vol. 225(1), pages 45-63, February.
    17. Trudeau, Christian & Vidal-Puga, Juan, 2020. "Clique games: A family of games with coincidence between the nucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 8-14.
    18. 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.
    19. Hougaard, Jens Leth & Tvede, Mich, 2022. "Trouble comes in threes: Core stability in minimum cost connection networks," European Journal of Operational Research, Elsevier, vol. 297(1), pages 319-324.
    20. Andreas Darmann & Christian Klamler & Ulrich Pferschy, 2015. "Sharing the Cost of a Path," Studies in Microeconomics, , vol. 3(1), pages 1-12, June.

    More about this item

    Keywords

    Minimum cost spanning tree problems; Demand operators; Irreducible cost matrix; Dutta–Kar rule; Prim algorithm;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:78:y:2024:i:1:d:10.1007_s00199-023-01526-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.