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Defining rules in cost spanning tree problems through the canonical form

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Author Info
Gustavo Bergantiños (Universidade de Vigo)
Juan Vidal-Puga (Universidade de Vigo)

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Abstract

We define the canonical form of a cost spanning tree problem. The canonical form has the property that reducing the cost of any arc, the minimal cost of connecting agents to the source is also reduced. We argue that the canonical form is a relevant concept in this kind of problems and study a rule using it. This rule satisfies much more interesting properties than other rules in the literature. Furthermore we provide two characterizations. Finally, we present several approaches to this rule without using the canonical form.

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Paper provided by EconWPA in its series Game Theory and Information with number 0402004.

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Date of creation: 12 Feb 2004
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Handle: RePEc:wpa:wuwpga:0402004

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Keywords: cost spanning tree problems canonical form rules;

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Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances

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References listed on IDEAS
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. Kar, Anirban, 2002. "Axiomatization of the Shapley Value on Minimum Cost Spanning Tree Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 265-277, February. [Downloadable!] (restricted)
  2. 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!]
  3. Feltkamp, V. & Tijs, S. & Muto, S., 1994. "Minimum Cost Spanning Extension Problems : The Proportional Rule and the Decentralized Rule," Discussion Paper 96, Tilburg University, Center for Economic Research. [Downloadable!]
  4. 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. [Downloadable!] (restricted)
    Other versions:
  5. 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)
    Other versions:
  6. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October. [Downloadable!] (restricted)
    Other versions:
  7. 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!]
  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. [Downloadable!] (restricted)
  9. Roger B. Myerson, 1978. "Conference Structures and Fair Allocation Rules," Discussion Papers 363, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  10. Daniel Granot & Michael Maschler, 1998. "Spanning network games," International Journal of Game Theory, Springer, vol. 27(4), pages 467-500. [Downloadable!] (restricted)
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Cited by:
(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, 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!]
  2. Gustavo Bergantiños & Juan Vidal-Puga, 2004. "Realizing efficient outcomes in cost spanning problems," Game Theory and Information 0403001, EconWPA. [Downloadable!]
  3. 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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