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Minimum cost spanning tree problems with indifferent agents

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  • Trudeau, Christian

Abstract

We consider an extension of minimum cost spanning tree (mcst) problems in which 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) 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 affected in the same manner if they have the same demand. If not, their changes are proportional to each other. We obtain a family of weighted Shapley values. Three interesting solutions in that family are characterized using stability, fairness and manipulation-proofness properties.

Suggested Citation

  • Trudeau, Christian, 2014. "Minimum cost spanning tree problems with indifferent agents," Games and Economic Behavior, Elsevier, vol. 84(C), pages 137-151.
    • Handle: RePEc:eee:gamebe:v:84:y:2014:i:c:p:137-151
    DOI: 10.1016/j.geb.2014.01.010
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    1. María Gómez-Rúa & Juan Vidal-Puga, 2011. "Merge-proofness in minimum cost spanning tree problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 309-329, May.
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    4. 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.
    5. 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.
    6. Trudeau, Christian, 2012. "A new stable and more responsive cost sharing solution for minimum cost spanning tree problems," Games and Economic Behavior, Elsevier, vol. 75(1), pages 402-412.
    7. Feltkamp, V. & Tijs, S.H. & Muto, S., 1994. "Minimum cost spanning extension problems : The proportional rule and the decentralized rule," Other publications TiSEM 2c6cd46b-7e72-4262-a479-3, Tilburg University, School of Economics and Management.
    8. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-1037, September.
    9. Hervé Moulin, 1995. "On Additive Methods To Share Joint Costs," The Japanese Economic Review, Japanese Economic Association, vol. 46(4), pages 303-332, December.
    10. 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.
    11. Trudeau, Christian, 2009. "Cost sharing with multiple technologies," Games and Economic Behavior, Elsevier, vol. 67(2), pages 695-707, November.
    12. Friedman, Eric & Moulin, Herve, 1999. "Three Methods to Share Joint Costs or Surplus," Journal of Economic Theory, Elsevier, vol. 87(2), pages 275-312, August.
    13. Eric Bahel & Christian Trudeau, 2013. "A discrete cost sharing model with technological cooperation," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 439-460, May.
    14. Rosenthal, Edward C., 2013. "Shortest path games," European Journal of Operational Research, Elsevier, vol. 224(1), pages 132-140.
    15. 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:

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    2. Bergantiños, Gustavo & Vidal-Puga, Juan, 2020. "Cooperative games for minimum cost spanning tree problems," MPRA Paper 104911, University Library of Munich, Germany.
    3. 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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    More about this item

    Keywords

    Minimum cost spanning tree; Steiner tree; Cost sharing; Weighted Shapley value;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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