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The Bird Core for Minimum Cost Spanning Tree problems Revisited: Monotonicity and Additivity Aspects

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  • Tijs, S.H.
  • Moretti, S.
  • Brânzei, R.
  • Norde, H.W.

    (Tilburg University, Center for Economic Research)

Abstract

A new way is presented to define for minimum cost spanning tree (mcst-) games the irreducible core, which is introduced by Bird in 1976.The Bird core correspondence turns out to have interesting monotonicity and additivity properties and each stable cost monotonic allocation rule for mcst-problems is a selection of the Bird core correspondence.Using the additivity property an axiomatic characterization of the Bird core correspondence is obtained.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2005-3.

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Date of creation: 2005
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Handle: RePEc:dgr:kubcen:20053

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References

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  1. Brânzei, R. & Tijs, S.H. & Timmer, J.B., 2001. "Information collecting situations and bi-monotonic allocation schemes," Open Access publications from Tilburg University urn:nbn:nl:ui:12-88210, Tilburg University.
  2. Juan J. Vidal-Puga & Gustavo Bergantiños, 2004. "Defining Rules in Cost Spanning Tree Problems Through the Canonical Form," Working Papers 2004.97, Fondazione Eni Enrico Mattei.
  3. Stefano Moretti & Henk Norde & Kim Pham Do & Stef Tijs, 2002. "Connection problems in mountains and monotonic allocation schemes," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 10(1), pages 83-99, June.
  4. Dragan, I. & Potters, J.A.M. & Tijs, S.H., 1989. "Superadditivity for solutions of coalitional games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154238, Tilburg University.
  5. Norde, H.W. & Moretti, S. & Tijs, S.H., 2004. "Minimum cost spanning tree games and population monotonic allocation schemes," Open Access publications from Tilburg University urn:nbn:nl:ui:12-123753, Tilburg University.
  6. 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, 04.
  7. Tijs, S.H. & Brânzei, R. & Moretti, S. & Norde, H.W., 2004. "Obligation Rules for Minimum Cost Spanning Tree Situations and their Monotonicity Properties," Discussion Paper 2004-53, Tilburg University, Center for Economic Research.
  8. Voorneveld, M. & Tijs, S.H. & Grahn, S., 2003. "Monotonic allocation schemes in clan games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-91573, Tilburg University.
  9. 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.
  10. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
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Cited by:
  1. 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.
  2. Bhaskar Dutta & Debasis Mishra, 2008. "Minimum cost arborescences," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 08-12, Indian Statistical Institute, New Delhi, India.
  3. Moretti, S. & Tijs, S.H. & Brânzei, R. & Norde, H.W., 2005. "Cost Monotonic "Cost and Charge" Rules for Connection Situations," Discussion Paper 2005-104, Tilburg University, Center for Economic Research.
  4. Hernández, Penélope & Peris, Josep E. & Silva-Reus, José A., 2012. "Strategic Sharing of a Costly Network," QM&ET Working Papers 12-10, Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica.

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