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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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Web page: http://center.uvt.nl

Related research

Keywords: cost allocation; minimum cost spanning tree games; Bird core; cost monotonicity; cone additivity;

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References

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  1. Voorneveld, M. & Tijs, S.H. & Grahn, S., 2000. "Monotonic Allocation Schemes in Clan Games," Discussion Paper 2000-80, Tilburg University, Center for Economic Research.
  2. 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.
  3. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
  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. 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.
  6. Norde, H.W. & Moretti, S. & Tijs, S.H., 2001. "Minimum Cost Spanning Tree Games and Population Monotonic Allocation Schemes," Discussion Paper 2001-18, Tilburg University, Center for Economic Research.
  7. 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.
  8. 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.
  9. Gustavo Bergantiños & Juan Vidal-Puga, 2004. "Defining rules in cost spanning tree problems through the canonical form," Game Theory and Information 0402004, EconWPA.
  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.
  11. 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.
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Cited by:
  1. Dutta, Bhaskar & Mishra, Debasis, 2012. "Minimum cost arborescences," Games and Economic Behavior, Elsevier, vol. 74(1), pages 120-143.
  2. 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.
  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. Moretti, Stefano, 2009. "Game Theory applied to gene expression analysis," Economics Papers from University Paris Dauphine 123456789/4922, Paris Dauphine University.

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