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Minimum cost spanning tree problems with indifferent agents

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  • Christian Trudeau

    ()
    (Department of Economics, University of Windsor)

Abstract

We consider an extension of minimum cost spanning tree (mcst) problems where some agents do not need to be connected to the source, but might reduce the cost of others to do so. Even if the cost usually cannot be computed in polynomial time, we extend the characterization of the Kar solution (Kar (2002, GEB)) for classic mcst problems. It is obtained by adapting the Equal treatment property: if the cost of the edge between two agents changes, their cost shares are a¤ected in the same manner if they have the same demand. If not, their changes are proportional to each other. We obtain three variations on the Kar solution, that are di¤erentiated and characterized using stability, fairness and manipulation-proofness properties.

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File URL: http://web2.uwindsor.ca/economics/RePEc/wis/pdf/1306.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 1306.

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Length: 17 pages
Date of creation: Aug 2013
Date of revision:
Handle: RePEc:wis:wpaper:1306

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Keywords: Minimum cost spanning tree; Steiner tree; cost sharing; Shapley value.;

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References

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  1. Eric Friedman & Moulin, Herve, 1995. "Three Methods to Share Joint Costs or Surplus," Working Papers 95-38, Duke University, Department of Economics.
  2. Trudeau, Christian, 2009. "Cost sharing with multiple technologies," Games and Economic Behavior, Elsevier, vol. 67(2), pages 695-707, November.
  3. MOULIN, Hervé & SPRUMONT, Yves., 2002. "Responsibility and Cross-Subsidization in Cost Sharing," Cahiers de recherche 2002-19, Universite de Montreal, Departement de sciences economiques.
  4. Moulin, Herve, 1995. "On Additive Methods to Share Joint Costs," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 98-99, August.
  5. 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.
  6. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
  7. Eric Bahel & Christian Trudeau, 2013. "A discrete cost sharing model with technological cooperation," International Journal of Game Theory, Springer, vol. 42(2), pages 439-460, May.
  8. Rosenthal, Edward C., 2013. "Shortest path games," European Journal of Operational Research, Elsevier, vol. 224(1), pages 132-140.
  9. 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.
  10. María Gómez-Rúa & Juan Vidal-Puga, 2011. "Merge-proofness in minimum cost spanning tree problems," International Journal of Game Theory, Springer, vol. 40(2), pages 309-329, May.
  11. 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.
  12. Trudeau, Christian, 2009. "Network flow problems and permutationally concave games," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 121-131, July.
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Cited by:
  1. Xiaojin Sun & Kwok Ping Tsang, 2013. "Housing Markets, Regulations and Monetary Policy," Working Papers e07-45, Virginia Polytechnic Institute and State University, Department of Economics.

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