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Characterizations of the cycle-complete and folk solutions for minimum cost spanning tree problems

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  • Christian Trudeau

    ()
    (Department of Economics, University of Windsor)

Abstract

Minimum cost spanning tree problems connect agents efficiently to a source when agents are located at different points and the cost of using an edge is fixed. The folk and cycle-complete cost sharing solutions always offer core allocations. We provide similar characterizations for both. A new property is based on the following observation: when all agents have the same cost to connect to the source, we can connect one of them to the source then connect all other agents to him, as if he was the source. Cost sharing should also be done in these two steps. We also use some common properties: Core Selection, Piecewise Linearity and an independence property. The solutions are differentiated by properties that apply when the cheapest edge to the source gets cheaper. Either the savings are equally distributed among all agents (folk) or the agent on that edge gets all of the savings (cycle-complete).

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File URL: http://web2.uwindsor.ca/economics/RePEc/wis/pdf/1303.pdf
File Function: First version, 2013
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Bibliographic Info

Paper provided by University of Windsor, Department of Economics in its series Working Papers with number 1303.

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Length: 16 pages
Date of creation: May 2013
Date of revision:
Handle: RePEc:wis:wpaper:1303

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Keywords: Minimum cost spanning tree problems; folk solution; cycle-complete solution; core.;

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  1. Bergantinos, Gustavo & Vidal-Puga, Juan J., 2007. "A fair rule in minimum cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 326-352, November.
  2. BergantiƱos, Gustavo & Vidal-Puga, Juan, 2009. "Additivity in minimum cost spanning tree problems," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 38-42, January.
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