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A characterization of optimistic weighted Shapley rules in minimum cost spanning tree problems

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  • Gustavo Bergantiños
  • Silvia Lorenzo-Freire

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  • Gustavo Bergantiños & Silvia Lorenzo-Freire, 2008. "A characterization of optimistic weighted Shapley rules in minimum cost spanning tree problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 523-538, June.
    • Handle: RePEc:spr:joecth:v:35:y:2008:i:3:p:523-538
    DOI: 10.1007/s00199-007-0248-1
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    References listed on IDEAS

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    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. 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.
    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. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Youngsub Chun, 2006. "No-envy in queueing problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 151-162, September.
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    Citations

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    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. 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.
    3. Ulrich Faigle & Michel Grabisch, 2012. "Values for Markovian coalition processes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 505-538, November.
    4. René Brink & P. Herings & Gerard Laan & A. Talman, 2015. "The Average Tree permission value for games with a permission tree," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 99-123, January.
    5. Bergantiños, Gustavo & Vidal-Puga, Juan, 2020. "Cooperative games for minimum cost spanning tree problems," MPRA Paper 104911, University Library of Munich, Germany.
    6. Csóka, Péter & Illés, Ferenc & Solymosi, Tamás, 2022. "On the Shapley value of liability games," European Journal of Operational Research, Elsevier, vol. 300(1), pages 378-386.
    7. 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.
    8. Bergantiños, Gustavo & Gómez-Rúa, María & Llorca, Natividad & Pulido, Manuel & Sánchez-Soriano, Joaquín, 2020. "Allocating costs in set covering problems," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1074-1087.
    9. René Brink & Chris Dietz & Gerard Laan & Genjiu Xu, 2017. "Comparable characterizations of four solutions for permission tree games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(4), pages 903-923, April.
    10. R. Pablo Arribillaga & G. Bergantiños, 2022. "Cooperative and axiomatic approaches to the knapsack allocation problem," Annals of Operations Research, Springer, vol. 318(2), pages 805-830, November.
    11. René Brink & Ilya Katsev & Gerard Laan, 2011. "Axiomatizations of two types of Shapley values for games on union closed systems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(1), pages 175-188, May.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Radzik, Tadeusz, 2012. "A new look at the role of players’ weights in the weighted Shapley value," European Journal of Operational Research, Elsevier, vol. 223(2), pages 407-416.
    18. Wei Li & Wolfgang Karl Hardle & Stefan Lessmann, 2022. "A Data-driven Case-based Reasoning in Bankruptcy Prediction," Papers 2211.00921, arXiv.org.
    19. María Gómez-Rúa & Juan Vidal-Puga, 2011. "Merge-proofness in minimum cost spanning tree problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 309-329, May.
    20. 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.
    21. 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.

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    More about this item

    Keywords

    Minimum cost spanning tree problems; Weighted Shapley values; C70; C71;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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