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Obligation rules for minimum cost spanning tree situations and their monotonicity properties

  • Tijs, Stef
  • Branzei, Rodica
  • Moretti, Stefano
  • Norde, Henk

We introduce the class of Obligation rules for minimum cost spanning tree situations.The main result of this paper is that such rules are cost monotonic and induce also population monotonic allocation schemes.Another characteristic of Obligation rules is that they assign to a minimum cost spanning tree situation a vector of cost contributions which can be obtained as product of a double stochastic matrix with the cost vector of edges in the optimal tree provided by the Kruskal algorithm.It turns out that the Potters value (P-value) is an element of this class.

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Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 175 (2006)
Issue (Month): 1 (November)
Pages: 121-134

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Handle: RePEc:eee:ejores:v:175:y:2006:i:1:p:121-134
Contact details of provider: Web page: http://www.elsevier.com/locate/eor

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  1. 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.
  2. Norde, Henk & Moretti, Stefano & Tijs, Stef, 2004. "Minimum cost spanning tree games and population monotonic allocation schemes," European Journal of Operational Research, Elsevier, vol. 154(1), pages 84-97, April.
  3. repec:dgr:kubcen:1994106 is not listed on IDEAS
  4. 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.
  5. Bhaskar Dutta & Anirban Kar, 2002. "Cost monotonicity, consistency and minimum cost spanning tree games," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 02-04, Indian Statistical Institute, New Delhi, India.
  6. repec:ner:tilbur:urn:nbn:nl:ui:12-123753 is not listed on IDEAS
  7. repec:ner:tilbur:urn:nbn:nl:ui:12-90092 is not listed on IDEAS
  8. 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.
  9. Pham Do, K.H. & Moretti, S. & Norde, H.W. & Tijs, S.H., 2002. "Connection problems in mountains and monotonic cost allocation schemes," Other publications TiSEM 98019ba4-13a2-470b-9850-f, Tilburg University, School of Economics and Management.
  10. 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.
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