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A non-cooperative approach to the cost spanning tree problem

Author

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  • Gustavo Bergantiños
  • Leticia Lorenzo

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Abstract

We associate to each cost spanning tree problem a non-cooperative game, which is inspired by a real-life problem. We study the Nash equilibria and subgame perfect Nash equilibria of this game. We prove that these equilibria are closely related with situations where agents connect sequentially to the source. Copyright Springer-Verlag 2004

Suggested Citation

  • 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.
  • Handle: RePEc:spr:mathme:v:59:y:2004:i:3:p:393-403
    DOI: 10.1007/s001860400352
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    File URL: http://hdl.handle.net/10.1007/s001860400352
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    Citations

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    Cited by:

    1. 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.
    2. Giménez Gómez, José M. (José Manuel) & Peris, Josep E. & Subiza, Begoña, 2019. "An egalitarian approach for sharing the cost of a spanning tree," Working Papers 2072/376029, Universitat Rovira i Virgili, Department of Economics.
    3. 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.
    4. 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.
    5. 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.
    6. Giménez Gómez, José M. (José Manuel) & Subiza, Begoña, 2016. "A `solidarity' approach to the problem of sharing a network cost," Working Papers 2072/290742, Universitat Rovira i Virgili, Department of Economics.
    7. 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.
    8. F. Fernández & J. Puerto, 2012. "The minimum cost shortest-path tree game," Annals of Operations Research, Springer, vol. 199(1), pages 23-32, October.
    9. Giménez Gómez, José M. (José Manuel) & Subiza, Begoña, 2016. "A `solidarity' approach to the problem of sharing a network cost," Working Papers 2072/290742, Universitat Rovira i Virgili, Department of Economics.
    10. 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.
    11. 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.
    12. Giménez Gómez, José M. (José Manuel) & Subiza, Begoña & Peris, Josep E., 2014. "Conflicting claims problem associated with cost sharing of a network," Working Papers 2072/242273, Universitat Rovira i Virgili, Department of Economics.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Giménez Gómez, José M. (José Manuel) & Subiza, Begoña & Peris, Josep E., 2014. "Conflicting claims problem associated with cost sharing of a network," Working Papers 2072/242273, Universitat Rovira i Virgili, Department of Economics.
    18. 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.
    19. 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.

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    Keywords

    Cost spanning tree problem; Equilibria;

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