IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v70y2009i3p451-463.html
   My bibliography  Save this article

Opportune moment strategies for a cost spanning tree game

Author

Listed:
  • F. Fernández
  • M. Hinojosa
  • A. Mármol
  • J. Puerto

Abstract

Cost spanning tree problems concern the construction of a tree which provides a connection with the source for every node of the network. In this paper, we address cost sharing problems associated to these situations when the agents located at the nodes act in a non-cooperative way. A class of strategies is proposed which produce minimum cost spanning trees and, at the same time, are strong Nash equilibria for a non-cooperative game associated to the problem. They are also subgame perfect Nash equilibria. Copyright Springer-Verlag 2009

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:70:y:2009:i:3:p:451-463
    DOI: 10.1007/s00186-008-0279-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-008-0279-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-008-0279-9?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. 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.
    2. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    3. Mutuswami, Suresh & Winter, Eyal, 2002. "Subscription Mechanisms for Network Formation," Journal of Economic Theory, Elsevier, vol. 106(2), pages 242-264, October.
    4. 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.
    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. F. Fernández & J. Puerto, 2012. "The minimum cost shortest-path tree game," Annals of Operations Research, Springer, vol. 199(1), pages 23-32, October.

    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. 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. Bergantiños, Gustavo & Vidal-Puga, Juan, 2020. "Cooperative games for minimum cost spanning tree problems," MPRA Paper 104911, University Library of Munich, Germany.
    4. 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.
    5. F. Fernández & J. Puerto, 2012. "The minimum cost shortest-path tree game," Annals of Operations Research, Springer, vol. 199(1), pages 23-32, October.
    6. 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.
    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. 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 & 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Estévez-Fernández, Arantza, 2012. "A game theoretical approach to sharing penalties and rewards in projects," European Journal of Operational Research, Elsevier, vol. 216(3), pages 647-657.
    16. Alparslan-Gok, S.Z. & Brânzei, R. & Tijs, S.H., 2008. "Cooperative Interval Games Arising from Airport Situations with Interval Data," Other publications TiSEM 5ded50b5-2a11-4d25-8511-b, Tilburg University, School of Economics and Management.
    17. Bloch, Francis & Jackson, Matthew O., 2007. "The formation of networks with transfers among players," Journal of Economic Theory, Elsevier, vol. 133(1), pages 83-110, March.
    18. Giulia Cesari & Roberto Lucchetti & Stefano Moretti, 2017. "Generalized additive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 919-939, November.
    19. van Beek, Andries & Malmberg, Benjamin & Borm, Peter & Quant, Marieke & Schouten, Jop, 2021. "Cooperation and Competition in Linear Production and Sequencing Processes," Discussion Paper 2021-011, Tilburg University, Center for Economic Research.
    20. Thijssen, J.J.J., 2003. "Investment under uncertainty, market evolution and coalition spillovers in a game theoretic perspective," Other publications TiSEM 672073a6-492e-4621-8d4a-0, Tilburg University, School of Economics and Management.

    More about this item

    Keywords

    Non-cooperative games; Spanning trees; Nash equilibria; C72; D85;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

    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:mathme:v:70:y:2009:i:3:p:451-463. 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.