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On the set of extreme core allocations for minimal cost spanning tree problems

Listed author(s):
  • Christian Trudeau

    ()

    (Department of Economics, University of Windsor)

  • Juan Vidal-Puga

    ()

    (Research Group of Economic Analysis and Departamento de Estatistica e IO, Universidade de Vigo)

Minimal cost spanning tree problems connect agents efficiently to a source when agents are located at different points and the cost of using an edge is fixed. We propose a method, based on the concept of marginal games, to generate all extreme points of the corresponding core. We show that three of the most famous solutions to share the cost of mcst problems, the Bird, folk and cycle-complete solutions, are closely related to our method.

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File URL: http://web2.uwindsor.ca/economics/RePEc/wis/pdf/1505.pdf
File Function: First version, 2015
Download Restriction: no

Paper provided by University of Windsor, Department of Economics in its series Working Papers with number 1505.

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Length: 32 pages
Date of creation: Nov 2015
Handle: RePEc:wis:wpaper:1505
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Phone: (519) 253-4232 ext 2368
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Web page: http://www.uwindsor.ca/economics/
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  1. 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.
  2. Marina Núñez & Carles Rafels, 1998. "On extreme points of the core and reduced games," Annals of Operations Research, Springer, vol. 84(0), pages 121-133, December.
  3. Juan J. Vidal-Puga, 2004. "Bargaining with commitments," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 129-144, January.
  4. Tijs, S.H., 2005. "The First Steps with Alexia, the Average Lexicographic Value," Discussion Paper 2005-123, Tilburg University, Center for Economic Research.
  5. Perez-Castrillo, David & Sotomayor, Marilda, 2002. "A Simple Selling and Buying Procedure," Journal of Economic Theory, Elsevier, vol. 103(2), pages 461-474, April.
  6. 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.
  7. Rodica Brânzei & Tamás Solymosi & Stef Tijs, 2005. "Strongly essential coalitions and the nucleolus of peer group games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 447-460, 09.
  8. 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.
  9. 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.
  10. Takumi Kongo & Yukihiko Funaki & Rodica Branzei & Stef Tijs, 2010. "Non-Cooperative And Axiomatic Characterizations Of The Average Lexicographic Value," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 417-435.
  11. 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.
  12. Christian Trudeau, 2013. "Characterizations Of The Kar And Folk Solutions For Minimum Cost Spanning Tree Problems," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-16.
  13. Hamers, Herbert & Klijn, Flip & Solymosi, Tamas & Tijs, Stef & Pere Villar, Joan, 2002. "Assignment Games Satisfy the CoMa-Property," Games and Economic Behavior, Elsevier, vol. 38(2), pages 231-239, February.
  14. Potters, Jos & Poos, Rene & Tijs, Stef & Muto, Shigeo, 1989. "Clan games," Games and Economic Behavior, Elsevier, vol. 1(3), pages 275-293, September.
  15. Trudeau, Christian, 2009. "Cost sharing with multiple technologies," Games and Economic Behavior, Elsevier, vol. 67(2), pages 695-707, November.
  16. Tijs, Stef & Borm, Peter & Lohmann, Edwin & Quant, Marieke, 2011. "An average lexicographic value for cooperative games," European Journal of Operational Research, Elsevier, vol. 213(1), pages 210-220, August.
  17. Funaki, Y. & Tijs, S.H. & Brânzei, R., 2007. "Leximals, the Lexicore and the Average Lexicographic Value," Discussion Paper 2007-97, Tilburg University, Center for Economic Research.
  18. Potters, J.A.M. & Poos, R. & Tijs, S.H. & Muto, S., 1989. "Clan games," Other publications TiSEM 1855e4e3-7392-4ef0-a073-8, Tilburg University, School of Economics and Management.
  19. Bahel, Eric & Trudeau, Christian, 2014. "Stable lexicographic rules for shortest path games," Economics Letters, Elsevier, vol. 125(2), pages 266-269.
  20. Kuipers, Jeroen, 1993. "On the Core of Information Graph Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 339-350.
  21. Nunez, Marina & Rafels, Carles, 2003. "Characterization of the extreme core allocations of the assignment game," Games and Economic Behavior, Elsevier, vol. 44(2), pages 311-331, August.
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