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

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Author Info
Tijs, S.H.
Branzei, R.
Moretti, S.
Norde, H.W. (Tilburg University, Center for Economic Research)

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Abstract

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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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 53.

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Date of creation: 2004
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Handle: RePEc:dgr:kubcen:200453

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. 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. [Downloadable!] (restricted)
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  2. Gustavo Bergantiños & Juan Vidal-Puga, 2004. "Additivity in cost spanning tree problems," Game Theory and Information 0405001, EconWPA. [Downloadable!]
  3. Branzei, R. & Moretti, S. & Norde, H.W. & Tijs, S.H., 2003. "The p-value for cost sharing in minimum cost spanning tree situations," Discussion Paper 129, Tilburg University, Center for Economic Research. [Downloadable!]
  4. 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. [Downloadable!] (restricted)
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  5. Feltkamp, V. & Tijs, S. & Muto, S., 1994. "On the Irreducible Core and the Equal Remaining Obligations Rule of Minimum Cost Spanning Extension Problems," Discussion Paper 106, Tilburg University, Center for Economic Research. [Downloadable!]
  6. 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. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Moretti, S. & Alparslan-Gok, S.Z. & Brânzei, R. & Tijs, S.H., 2008. "Connection Situations under Uncertainty," Discussion Paper 2008-64, Tilburg University, Center for Economic Research. [Downloadable!]
  2. Moretti, Stefano & Tijs, Stef & Branzei, Rodica & ...,, 2005. "Cost monotonic 'Construct and Charge' rules for connection situations," Discussion Paper 104, Tilburg University, Center for Economic Research. [Downloadable!]
  3. Ciftci, B.B. & Tijs, S.H., 2007. "A Vertex Oriented Approach to Minimum Cost Spanning Tree Problems," Discussion Paper 2007-89, Tilburg University, Center for Economic Research. [Downloadable!]
  4. Gomez-Rua, Maria & Vidal-Puga, Juan, 2006. "No advantageous merging in minimum cost spanning tree problems," MPRA Paper 601, University Library of Munich, Germany. [Downloadable!]
  5. Leticia Lorenzo & Silvia Lorenzo-Freire, 2009. "A characterization of Kruskal sharing rules for minimum cost spanning tree problems," International Journal of Game Theory, Springer, vol. 38(1), pages 107-126, March. [Downloadable!] (restricted)
  6. Tijs, Stef & Moretti, Stefano & Branzei, Rodica & Norde, Henk, 2005. "The Bird core for minimum cost spanning tree problems revisited: monotonicity and additivity aspects," Discussion Paper 3, Tilburg University, Center for Economic Research. [Downloadable!]
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