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An axiomatic approach in minimum cost spanning tree problems with groups

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  • Gustavo Bergantiños
  • María Gómez-Rúa

Abstract

We study minimum cost spanning tree problems with groups, where agents are located in different villages, cities, etc. The groups are formed by agents living in the same village. In Bergantiños and Gómez-Rúa (Economic Theory 43:227–262, 2010 ) we define the rule F as the Owen value of the irreducible game with groups and we prove that F generalizes the folk rule of minimum cost spanning tree problems. Bergantiños and Vidal-Puga (Journal of Economic Theory 137:326–352, 2007a ) give two characterizations of the folk rule. In the first one they characterize it as the unique rule satisfying cost monotonicity, population monotonicity and equal share of extra costs. In the second characterization of the folk rule they replace cost monotonicity by independence of irrelevant trees and population monotonicity by separability. In this paper we extend such characterizations to our setting. Some of the properties are the same (cost monotonicity and independence of irrelevant trees) and the other need to be adapted. In general, we do it by claiming the property twice: once among the groups and the other among the agents inside the same group. Copyright Springer Science+Business Media New York 2015

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  • 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.
    • Handle: RePEc:spr:annopr:v:225:y:2015:i:1:p:45-63:10.1007/s10479-012-1251-x
    DOI: 10.1007/s10479-012-1251-x
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    References listed on IDEAS

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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 & 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.
    3. 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.
    4. Pulido, Manuel A. & Sánchez-Soriano, Joaquín, 2009. "On the core, the Weber set and convexity in games with a priori unions," European Journal of Operational Research, Elsevier, vol. 193(2), pages 468-475, March.
    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. 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.
    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. Gómez-Rúa, María & Vidal-Puga, Juan, 2010. "The axiomatic approach to three values in games with coalition structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 795-806, December.
    9. 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.
    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. Albizuri, M. Josune, 2009. "Generalized coalitional semivalues," European Journal of Operational Research, Elsevier, vol. 196(2), pages 578-584, July.
    13. 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.
    14. Bogomolnaia, Anna & Moulin, Hervé, 2010. "Sharing a minimal cost spanning tree: Beyond the Folk solution," Games and Economic Behavior, Elsevier, vol. 69(2), pages 238-248, July.
    15. Stefano Moretti & Rodica Branzei & Henk Norde & Stef Tijs, 2004. "The P-value for cost sharing in minimum," Theory and Decision, Springer, vol. 56(1), pages 47-61, April.
    16. 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.
    17. 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.
    18. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    19. 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.
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