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Characterization of monotonic rules in minimum cost spanning tree problems

Listed author(s):
  • Gustavo Bergantiños

    ()

  • Juan Vidal-Puga

We provide, in minimum cost spanning tree problems, a general framework to identify the family of rules satisfying monotonicity over cost and population. We also prove that the set of allocations induced by the family coincides with the so-called irreducible core, that results from decreasing the cost of the arcs as much as possible, without reducing the minimal cost. Copyright Springer-Verlag Berlin Heidelberg 2015

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File URL: http://hdl.handle.net/10.1007/s00182-014-0456-4
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Article provided by Springer & Game Theory Society in its journal International Journal of Game Theory.

Volume (Year): 44 (2015)
Issue (Month): 4 (November)
Pages: 835-868

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Handle: RePEc:spr:jogath:v:44:y:2015:i:4:p:835-868
DOI: 10.1007/s00182-014-0456-4
Contact details of provider: Web page: http://www.springer.com

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  1. 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.
  2. 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.
  3. Tijs, Stef & Branzei, Rodica & Moretti, Stefano & Norde, Henk, 2006. "Obligation rules for minimum cost spanning tree situations and their monotonicity properties," European Journal of Operational Research, Elsevier, vol. 175(1), pages 121-134, November.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. Kar, Anirban, 2002. "Axiomatization of the Shapley Value on Minimum Cost Spanning Tree Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 265-277, February.
  9. 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.
  10. Stefano Moretti & Rodica Branzei & Henk Norde & Stef Tijs, 2004. "The P-value for cost sharing in minimum," Theory and Decision, Springer, vol. 56(2_2), pages 47-61, February.
  11. 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.
  12. Leticia Lorenzo & Silvia Lorenzo-Freire, 2009. "A characterization of Kruskal sharing rules for minimum cost spanning tree problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 107-126, March.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. repec:spr:compst:v:59:y:2004:i:3:p:393-403 is not listed on IDEAS
  19. 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.
  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.
  21. 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.
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