IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v307y2023i2p922-928.html
   My bibliography  Save this article

A non-cooperative approach to the folk rule in minimum cost spanning tree problems

Author

Listed:
  • Hernández, Penélope
  • Peris, Josep E.
  • Vidal-Puga, Juan

Abstract

This paper deals with the problem of finding a way to distribute the cost of a minimum cost spanning tree problem between the players. A rule that assigns a payoff to each player provides this distribution. An optimistic point of view is considered to devise a cooperative game. Following this optimistic approach, a sequential game provides this construction to define the action sets of the players. The main result states the existence of a unique cost allocation in subgame perfect equilibria. This cost allocation matches the one suggested by the folk rule.

Suggested Citation

  • Hernández, Penélope & Peris, Josep E. & Vidal-Puga, Juan, 2023. "A non-cooperative approach to the folk rule in minimum cost spanning tree problems," European Journal of Operational Research, Elsevier, vol. 307(2), pages 922-928.
    • Handle: RePEc:eee:ejores:v:307:y:2023:i:2:p:922-928
    DOI: 10.1016/j.ejor.2022.09.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221722007445
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2022.09.015?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Hougaard, Jens Leth & Tvede, Mich, 2012. "Truth-telling and Nash equilibria in minimum cost spanning tree models," European Journal of Operational Research, Elsevier, vol. 222(3), pages 566-570.
    3. 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.
    4. 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.
    5. Norde, Henk & Moretti, Stefano & Tijs, Stef, 2004. "Minimum cost spanning tree games and population monotonic allocation schemes," European Journal of Operational Research, Elsevier, vol. 154(1), pages 84-97, April.
    6. Roberto Serrano, 2021. "Sixty-seven years of the Nash program: time for retirement?," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 35-48, March.
    7. Mutuswami, Suresh & Winter, Eyal, 2002. "Subscription Mechanisms for Network Formation," Journal of Economic Theory, Elsevier, vol. 106(2), pages 242-264, October.
    8. 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.
    9. 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.
    10. Bag, Parimal Kanti & Winter, Eyal, 1999. "Simple Subscription Mechanisms for Excludable Public Goods," Journal of Economic Theory, Elsevier, vol. 87(1), pages 72-94, July.
    11. Dutta, Bhaskar & Mishra, Debasis, 2012. "Minimum cost arborescences," Games and Economic Behavior, Elsevier, vol. 74(1), pages 120-143.
    12. 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.
    13. Gustavo Bergantiños & Juan Vidal-Puga, 2007. "The optimistic TU game in minimum cost spanning tree problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 223-239, October.
    14. 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.
    15. Moulin, Hervé & Velez, Rodrigo A., 2013. "The price of imperfect competition for a spanning network," Games and Economic Behavior, Elsevier, vol. 81(C), pages 11-26.
    16. Bogomolnaia, Anna & Moulin, Hervé, 2010. "Sharing a minimal cost spanning tree: Beyond the Folk solution," Games and Economic Behavior, Elsevier, vol. 69(2), pages 238-248, July.
    17. Gustavo Bergantinos & Juan Vidal-Puga, 2008. "On Some Properties of Cost Allocation Rules in Minimum Cost Spanning Tree Problems," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 2(3), pages 251-267, December.
    18. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    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. 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.
    2. Bergantiños, Gustavo & Vidal-Puga, Juan, 2020. "Cooperative games for minimum cost spanning tree problems," MPRA Paper 104911, University Library of Munich, Germany.
    3. 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.
    4. Dutta, Bhaskar & Mishra, Debasis, 2012. "Minimum cost arborescences," Games and Economic Behavior, Elsevier, vol. 74(1), pages 120-143.
    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. 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.
    7. 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.
    8. Christian Trudeau, 2014. "Linking the Kar and folk solutions through a problem separation property," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 845-870, November.
    9. Kusunoki, Yoshifumi & Tanino, Tetsuzo, 2017. "Investigation on irreducible cost vectors in minimum cost arborescence problems," European Journal of Operational Research, Elsevier, vol. 261(1), pages 214-221.
    10. 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.
    11. Moulin, Hervé, 2014. "Pricing traffic in a spanning network," Games and Economic Behavior, Elsevier, vol. 86(C), pages 475-490.
    12. Jens Hougaard & Hervé Moulin & Lars Østerdal, 2010. "Decentralized pricing in minimum cost spanning trees," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(2), pages 293-306, August.
    13. Bogomolnaia, Anna & Moulin, Hervé, 2010. "Sharing a minimal cost spanning tree: Beyond the Folk solution," Games and Economic Behavior, Elsevier, vol. 69(2), pages 238-248, July.
    14. Hougaard, Jens Leth & Tvede, Mich, 2012. "Truth-telling and Nash equilibria in minimum cost spanning tree models," European Journal of Operational Research, Elsevier, vol. 222(3), pages 566-570.
    15. Eric Bahel & Christian Trudeau, 2016. "From spanning trees to arborescences: new and extended cost sharing solutions," Working Papers 1601, University of Windsor, Department of Economics.
    16. Bergantiños, G. & Gómez-Rúa, M. & Llorca, N. & Pulido, M. & Sánchez-Soriano, J., 2014. "A new rule for source connection problems," European Journal of Operational Research, Elsevier, vol. 234(3), pages 780-788.
    17. 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.
    18. Chun, Youngsub & Lee, Joosung, 2012. "Sequential contributions rules for minimum cost spanning tree problems," Mathematical Social Sciences, Elsevier, vol. 64(2), pages 136-143.
    19. Bergantiños, Gustavo & Martínez, Ricardo, 2014. "Cost allocation in asymmetric trees," European Journal of Operational Research, Elsevier, vol. 237(3), pages 975-987.
    20. 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.

    More about this item

    Keywords

    Game theory; Minimum cost spanning tree; Cost allocation; Subgame perfect equilibrium;
    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

    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:eee:ejores:v:307:y:2023:i:2:p:922-928. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.