International Journal of Game Theory

, Volume 40, Issue 2, pp 309–329 | Cite as

Merge-proofness in minimum cost spanning tree problems

Original Paper

Abstract

In the context of cost sharing in minimum cost spanning tree problems, we introduce a property called merge-proofness. This property says that no group of agents can be better off claiming to be a single node. We show that the sharing rule that assigns to each agent his own connection cost (the Bird rule) satisfies this property. Moreover, we provide a characterization of the Bird rule using merge-proofness.

Keywords

Minimum cost spanning tree problems Cost sharing Bird rule Merge-proofness 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aarts H, Driessen T (1993) The irreducible core of a minimum cost spanning tree game. Math Methods Oper Res 38: 163–174CrossRefGoogle Scholar
  2. Bergantiños G, Lorenzo-Freire S (2008) Optimistic weighted Shapley rules in minimum cost spanning tree problems. Eur J Oper Res 185: 289–298CrossRefGoogle Scholar
  3. Bergantiños G, Vidal-Puga J (2004) The folk solution and Boruvka’s algorithm in minimum cost spanning tree problems. Mimeo. http://webs.uvigo.es/vidalpuga
  4. Bergantiños G, Vidal-Puga J (2007a) A fair rule in minimum cost spanning tree problems. J Econ Theory 137(1): 326–352. doi:10.1016/j.jet.2006.11.001 CrossRefGoogle Scholar
  5. Bergantiños G, Vidal-Puga J (2007b) The optimistic TU game in minimum cost spanning tree problems. Int J Game Theory 36(2): 223–239. doi:10.1007/s00182-006-0069-7 CrossRefGoogle Scholar
  6. Bird CG (1976) On cost allocation for a spanning tree: a game theoretic approach. Networks 6: 335–350CrossRefGoogle Scholar
  7. Branzei R, Moretti S, Norde H, Tijs S (2004) The P-value for cost sharing in minimum cost spanning tree situations. Theory Decis 56: 47–61CrossRefGoogle Scholar
  8. Derks J, Haller H (1999) Null players out? Linear values for games with variable supports. Int Game Theory Rev 1(3&4): 301–314CrossRefGoogle Scholar
  9. Dutta B, Kar A (2004) Cost monotonicity, consistency and minimum cost spanning tree games. Games Econ Behav 48(2): 223–248CrossRefGoogle Scholar
  10. Feltkamp V, Tijs S, Muto S (1994) On the irreducible core and the equal remaining obligation rule of minimum cost extension problems. Tilburg University, MimeoGoogle Scholar
  11. Granot D, Huberman G (1981) Minimum cost spanning tree games. Math Programm 21: 1–18CrossRefGoogle Scholar
  12. Granot D, Huberman G (1984) On the core and nucleolus of the minimum cost spanning tree games. Math Programm 29: 323–347CrossRefGoogle Scholar
  13. Hamiache G (2006) A value for games with coalition structures. Soc Choice Welfare 26: 93–105CrossRefGoogle Scholar
  14. Kar A (2002) Axiomatization of the Shapley value on minimum cost spanning tree games. Games Econ Behav 38: 265–277CrossRefGoogle Scholar
  15. Norde H, Moretti S, Tijs S (2004) Minimum cost spanning tree games and population monotonic allocation schemes. Eur J Oper Res 154: 84–97CrossRefGoogle Scholar
  16. O’Neill B (1982) A problem of rights arbitration from the Talmud. Math Soc Sci 2: 345–371CrossRefGoogle Scholar
  17. Özsoy H (2006) A characterization of Bird’s rule. Rice University, MimeoGoogle Scholar
  18. Prim RC (1957) Shortest connection networks and some generalizations. Bell Syst Technol J 36: 1389–1401Google Scholar
  19. Sharkey WW (1995) Networks models in economics. In: Handbooks of operation research and management science. Networks, vol 8, Chap 9. North Holland, AmsterdamGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Departamento de Estatística e Investigación OperativaUniversidade de VigoVigoSpain
  2. 2.Research Group in Economic AnalysisUniversidade de VigoVigoSpain

Personalised recommendations