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On the Core of Cost-Revenue Games: Minimum Cost Spanning Tree Games with Revenues

Author

Listed:
  • Arantza Estevez-Fernandez

    (VU University Amsterdam)

  • Hans Reijnierse

    (CentER, Tilburg University)

Abstract

This discussion paper led to an article in 'European Journal of Operational Research' , (2014), 237, 606-616. In this paper, we analyze cost sharing problems arising from a general service by explicitly taking into account the generated revenues. To this cost-revenue sharing problem, we associate a cooperative game with transferable utility, called cost-revenue game. By considering cooperation among the agents using the general service, the value of a coalition is defined as the maximum net profit that the coalition may obtain by means of cooperation. As a result, a coalition may profit from not allowing all its members to get the service that generates the revenues. We focus on the study of the core of cost-revenue games. Under the assumption that cooperation among the members of the grand coalition grants the use of the service under consideration to all its members, it is shown that a cost-revenue game has a non-empty core for any vector of revenues if, and only if, the dual game of the cost game has a large core. Using this result, we investigate minimum cost spanning tree games with revenues. We show that if every connection cost can take only two values (low or high cost), then, the corresponding minimum cost spanning tree game with revenues has a non-empty core. Furthermore, we provide an example of a minimum cost spanning tree game with revenues with an empty core where every connection cost can take only one of three values (low, medium, or high cost).

Suggested Citation

  • Arantza Estevez-Fernandez & Hans Reijnierse, 2012. "On the Core of Cost-Revenue Games: Minimum Cost Spanning Tree Games with Revenues," Tinbergen Institute Discussion Papers 12-101/II, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20120101
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    References listed on IDEAS

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    1. Moretti, S., 2008. "Cost allocation problems arising from connection situations in an interactive cooperative setting," Other publications TiSEM 2d63e0bf-18b7-4695-bdee-e, Tilburg University, School of Economics and Management.
    2. Norde, Henk & Moretti, Stefano & Tijs, Stef, 2004. "Minimum cost spanning tree games and population monotonic allocation schemes," European Journal of Operational Research, Elsevier, vol. 154(1), pages 84-97, April.
    3. Arantza Estévez-Fernández & Peter Borm & Marc Meertens & Hans Reijnierse, 2009. "On the core of routing games with revenues," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 291-304, June.
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    8. M. Meertens & J. Potters, 2006. "The nucleolus of trees with revenues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 363-382, October.
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    11. Potters, J.A.M. & Curiel, I. & Tijs, S.H., 1992. "Traveling salesman games," Other publications TiSEM 0dd4cf3d-25fa-4179-80f6-6, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Subiza, Begoña & Giménez, José Manuel & Peris, Josep E., 2015. "Folk solution for simple minimum cost spanning tree problems," QM&ET Working Papers 15-7, University of Alicante, D. Quantitative Methods and Economic Theory.

    More about this item

    Keywords

    Cost-revenue allocation problem; cooperative game; core; minimum cost spanning tree problem;

    JEL classification:

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

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