IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v137y2005i1p101-11510.1007-s10479-005-2248-5.html
   My bibliography  Save this article

Optimal Equilibria in the Non-Cooperative Game Associated with Cost Spanning Tree Problems

Author

Listed:
  • Gustavo Bergantiños
  • Leticia Lorenzo

Abstract

We study the Pareto optimal equilibria payoffs of the non-cooperative game associated with the cost spanning tree problem. We give two characterisations of these payoffs: one based on the tree they induce and another based on the strategies played by agents. Moreover, an algorithm for computing all these payoffs is provided. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • Gustavo Bergantiños & Leticia Lorenzo, 2005. "Optimal Equilibria in the Non-Cooperative Game Associated with Cost Spanning Tree Problems," Annals of Operations Research, Springer, vol. 137(1), pages 101-115, July.
    • Handle: RePEc:spr:annopr:v:137:y:2005:i:1:p:101-115:10.1007/s10479-005-2248-5
    DOI: 10.1007/s10479-005-2248-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-005-2248-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-005-2248-5?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. Gustavo Bergantiños & Leticia Lorenzo, 2004. "A non-cooperative approach to the cost spanning tree problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(3), pages 393-403, July.
    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. Gustavo Bergantiños & María Gómez-Rúa, 2010. "Minimum cost spanning tree problems with groups," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(2), pages 227-262, May.
    2. Gustavo Bergantiños & Leticia Lorenzo, 2008. "Noncooperative cost spanning tree games with budget restrictions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(8), pages 747-757, December.
    3. Jens Leth Hougaard & Mich Tvede, 2020. "Implementation of Optimal Connection Networks," IFRO Working Paper 2020/06, University of Copenhagen, Department of Food and Resource Economics.
    4. Bergantiños, Gustavo & Vidal-Puga, Juan, 2009. "Additivity in minimum cost spanning tree problems," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 38-42, January.
    5. 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.
    6. 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.
    7. Hougaard, Jens Leth & Tvede, Mich, 2015. "Minimum cost connection networks: Truth-telling and implementation," Journal of Economic Theory, Elsevier, vol. 157(C), pages 76-99.
    8. Jens Leth Hougaard & Mich Tvede, 2020. "Trouble Comes in Threes: Core stability in Minimum Cost Connection Networks," IFRO Working Paper 2020/07, University of Copenhagen, Department of Food and Resource Economics.
    9. Bergantiños, Gustavo & Vidal-Puga, Juan, 2020. "Cooperative games for minimum cost spanning tree problems," MPRA Paper 104911, University Library of Munich, Germany.
    10. 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.
    11. F. Fernández & J. Puerto, 2012. "The minimum cost shortest-path tree game," Annals of Operations Research, Springer, vol. 199(1), pages 23-32, October.
    12. 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.
    13. 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.
    14. 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.
    15. F. Fernández & M. Hinojosa & A. Mármol & J. Puerto, 2009. "Opportune moment strategies for a cost spanning tree game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(3), pages 451-463, December.

    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, 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.
    2. F. Fernández & J. Puerto, 2012. "The minimum cost shortest-path tree game," Annals of Operations Research, Springer, vol. 199(1), pages 23-32, October.
    3. Álvarez, Xana & Gómez-Rúa, María & Vidal-Puga, Juan, 2019. "Risk prevention of land flood: A cooperative game theory approach," MPRA Paper 91515, University Library of Munich, Germany.
    4. 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.
    5. Jens Leth Hougaard & Mich Tvede, 2010. "Strategyproof Nash Equilibria in Minimum Cost Spanning Tree Models," MSAP Working Paper Series 01_2010, University of Copenhagen, Department of Food and Resource Economics.
    6. Hougaard, Jens Leth & Tvede, Mich, 2015. "Minimum cost connection networks: Truth-telling and implementation," Journal of Economic Theory, Elsevier, vol. 157(C), pages 76-99.
    7. Gustavo Bergantiños & Juan Vidal-Puga, 2004. "Realizing efficient outcomes in cost spanning problems," Game Theory and Information 0403001, University Library of Munich, Germany.
    8. 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.
    9. 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.
    10. 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.
    11. Alfredo Valencia-Toledo & Juan Vidal-Puga, 2020. "A sequential bargaining protocol for land rental arrangements," Review of Economic Design, Springer;Society for Economic Design, vol. 24(1), pages 65-99, June.
    12. F. Fernández & M. Hinojosa & A. Mármol & J. Puerto, 2009. "Opportune moment strategies for a cost spanning tree game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(3), pages 451-463, December.
    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. 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.
    15. 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.
    16. Gustavo Bergantiños & María Gómez-Rúa, 2010. "Minimum cost spanning tree problems with groups," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(2), pages 227-262, May.
    17. Jens Leth Hougaard & Mich Tvede, 2020. "Implementation of Optimal Connection Networks," IFRO Working Paper 2020/06, University of Copenhagen, Department of Food and Resource Economics.
    18. Giménez-Gómez, José-Manuel & Subiza, Begoña & Peris, Josep, 2014. "Conflicting Claims Problem Associated with Cost Sharing of a Network," QM&ET Working Papers 14-3, University of Alicante, D. Quantitative Methods and Economic Theory.
    19. 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.
    20. Bergantinos, Gustavo & Lorenzo-Freire, Silvia, 2008. ""Optimistic" weighted Shapley rules in minimum cost spanning tree problems," European Journal of Operational Research, Elsevier, vol. 185(1), pages 289-298, February.

    More about this item

    Keywords

    cost spanning tree problem; optimality;

    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:annopr:v:137:y:2005:i:1:p:101-115:10.1007/s10479-005-2248-5. 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.