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Additivity in minimum cost spanning tree problems

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  • Bergantiños, Gustavo
  • Vidal-Puga, Juan

Abstract

We characterize a rule in minimum cost spanning tree problems using an additivity property and some basic properties. If the set of possible agents has at least three agents, these basic properties are symmetry and separability. If the set of possible agents has two agents, we must add positivity.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:mateco:v:45:y:2009:i:1-2:p:38-42
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    References listed on IDEAS

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    1. Dutta, Bhaskar & Kar, Anirban, 2004. "Cost monotonicity, consistency and minimum cost spanning tree games," Games and Economic Behavior, Elsevier, pages 223-248.
    2. 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.
    3. 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.
    4. Brânzei, R. & Moretti, S. & Norde, H.W. & Tijs, S.H., 2003. "The P-Value for Cost Sharing in Minimum Cost Spanning Tree Situations," Discussion Paper 2003-129, Tilburg University, Center for Economic Research.
    5. 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.
    6. 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.
    7. Daniel Granot & Michael Maschler, 1998. "Spanning network games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(4), pages 467-500.
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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, 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.
    3. María Gómez-Rúa, 2012. "Sharing a polluted river network through environmental taxes," Economics Bulletin, AccessEcon, vol. 32(1), pages 992-1000.
    4. repec:spr:sochwe:v:49:y:2017:i:2:d:10.1007_s00355-017-1061-9 is not listed on IDEAS
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. María Gómez-Rúa, 2013. "Sharing a polluted river through environmental taxes," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 4(2), pages 137-153, June.
    10. 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.
    11. Gustavo Bergantiños & Leticia Lorenzo & Silvia Lorenzo-Freire, 2010. "The family of cost monotonic and cost additive rules in minimum cost spanning tree problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(4), pages 695-710, April.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.

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