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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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Suggested Citation

  • 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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    Cited by:

    1. Eric Bahel & Christian Trudeau, 2018. "Stable cost sharing in production allocation games," Review of Economic Design, Springer;Society for Economic Design, vol. 22(1), pages 25-53, June.
    2. Streekstra, Leanne & Trudeau, Christian, 2020. "Stable source connection and assignment problems as multi-period shortest path problems," Discussion Papers on Economics 7/2020, University of Southern Denmark, 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. Kleppe, J. & Reijnierse, J.H., 2007. "Public Congestion Network Situations, and Related Games," Other publications TiSEM 2ee69f43-48b2-4c19-add5-8, Tilburg University, School of Economics and Management.
    5. Quant, M. & Reijnierse, J.H., 2004. "Convex Congestion Network Problems," Other publications TiSEM 4de27e1f-abe0-40c1-8369-2, Tilburg University, School of Economics and Management.
    6. Trudeau, Christian, 2009. "Network flow problems and permutationally concave games," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 121-131, July.
    7. Cheng Wan, 2016. "Strategic decentralization in binary choice composite congestion games," Post-Print hal-02885837, HAL.
    8. Kleppe, J. & Reijnierse, J.H., 2007. "Public Congestion Network Situations, and Related Games," Discussion Paper 2007-58, Tilburg University, Center for Economic Research.
    9. Bahel, Eric & Trudeau, Christian, 2019. "A cost sharing example in which subsidies are necessary for stability," Economics Letters, Elsevier, vol. 185(C).
    10. 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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