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Congestion network problems and related games

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  • Quant, Marieke
  • Borm, Peter
  • Reijnierse, Hans

Abstract

This paper analyzes network problems with congestion effects from a cooperative game theoretic perspective.It is shown that for network problems with convex congestion costs, the corresponding games have a non-empty core.If congestion costs are concave, then the corresponding game has not necessarily core elements, but it is derived that, contrary to the convex congestion situation, there always exist optimal tree networks.Extensions of these results to a class of relaxed network problems and associated games are derived.
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  • Quant, Marieke & Borm, Peter & Reijnierse, Hans, 2006. "Congestion network problems and related games," European Journal of Operational Research, Elsevier, vol. 172(3), pages 919-930, August.
  • Handle: RePEc:eee:ejores:v:172:y:2006:i:3:p:919-930
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    7. Brânzei, R. & Moretti, S. & Norde, H.W. & Tijs, S.H., 2003. "The P-Value for Cost Sharing in Minimum Cost Spanning Tree Situations," Discussion Paper 2003-129, Tilburg University, Center for Economic Research.
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    Cited by:

    1. Kleppe, J. & Reijnierse, J.H., 2007. "Public Congestion Network Situations, and Related Games," Discussion Paper 2007-58, Tilburg University, Center for Economic Research.
    2. Eric Bahel & Christian Trudeau, 2014. "Stable cost sharing in production allocation games," Working Papers 1402, University of Windsor, Department of Economics.
    3. Wan, Cheng, 2016. "Strategic decentralization in binary choice composite congestion games," European Journal of Operational Research, Elsevier, vol. 250(2), pages 531-542.
    4. Quant, M. & Reijnierse, J.H., 2004. "Convex Congestion Network Problems," Discussion Paper 2004-59, Tilburg University, Center for Economic Research.
    5. Trudeau, Christian, 2009. "Network flow problems and permutationally concave games," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 121-131, July.
    6. Bergantiños, G. & Gómez-Rúa, M. & Llorca, N. & Pulido, M. & Sánchez-Soriano, J., 2014. "A new rule for source connection problems," European Journal of Operational Research, Elsevier, vol. 234(3), pages 780-788.

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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