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A Vertex Oriented Approach to Minimum Cost Spanning Tree Problems

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Author Info
Ciftci, B.B.
Tijs, S.H. (Tilburg University, Center for Economic Research)
Abstract

In this paper we consider spanning tree problems, where n players want to be connected to a source as cheap as possible. We introduce and analyze (n!) vertex oriented construct and charge procedures for such spanning tree situations leading in n steps to a minimum cost spanning tree and a cost sharing where each player pays the edge which he chooses in the procedure. The main result of the paper is that the average of the n! cost sharings provided by our procedure is equal to the P-value for minimum cost spanning tree situations introduced and characterized by Branzei et al. (2004). As a side product, we find a new method, the vertex oriented procedure, to construct minimum cost spanning trees.

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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2007-89.

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Date of creation: 2007
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Handle: RePEc:dgr:kubcen:200789

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Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Models of Political Processes: Rent-seeking, Elections, Legislatures, and Voting Behavior

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  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. 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)
  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)
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  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)
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  6. 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. [Downloadable!] (restricted)
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  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. 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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  9. Gustavo Bergantiños & Juan Vidal-Puga, 2007. "The optimistic TU game in minimum cost spanning tree problems," International Journal of Game Theory, Springer, vol. 36(2), pages 223-239, October. [Downloadable!] (restricted)
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