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Convexity of Network Restricted Games Induced by Minimum Partitions

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  • Alexandre Skoda

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider restricted games on weighted communication graphs associated with minimum partitions. We replace in the classical definition of Myerson's graph-restricted game the connected components of any subgraph by the sub-components corresponding to a minimum partition. This minimum partition P min is induced by the deletion of the minimum weight edges. We provide necessary conditions on the graph edge-weights to have inheritance of convexity from the underlying game to the restricted game associated with P min. Then we establish that these conditions are also sufficient for a weaker condition, called F-convexity, obtained by restriction of convexity to connected subsets. Moreover we show that Myerson's game associated to a given graph G can be obtained as a particular case of the P min-restricted game for a specific weighted graph G ′. Then we prove that G is cycle-complete if and only if a specific condition on adjacent cycles is satisfied on G ′ .

Suggested Citation

  • Alexandre Skoda, 2016. "Convexity of Network Restricted Games Induced by Minimum Partitions," Post-Print hal-01305005, HAL.
    • Handle: RePEc:hal:journl:hal-01305005
    Note: View the original document on HAL open archive server: https://hal.science/hal-01305005
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    References listed on IDEAS

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    1. E. Algaba & J. M. Bilbao & P. Borm & J. J. López, 2000. "The position value for union stable systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(2), pages 221-236, November.
    2. M. Grabisch & A. Skoda, 2012. "Games induced by the partitioning of a graph," Annals of Operations Research, Springer, vol. 201(1), pages 229-249, December.
    3. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
    4. repec:hal:pseose:hal-00830291 is not listed on IDEAS
    5. Faigle, U. & Grabisch, M. & Heyne, M., 2010. "Monge extensions of cooperation and communication structures," European Journal of Operational Research, Elsevier, vol. 206(1), pages 104-110, October.
    6. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    7. van den Nouweland, Anne & Borm, Peter, 1991. "On the Convexity of Communication Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(4), pages 421-430.
    8. E. Algaba & J.M. Bilbao & J.J. López, 2001. "A unified approach to restricted games," Theory and Decision, Springer, vol. 50(4), pages 333-345, June.
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    Cited by:

    1. Alexandre Skoda, 2017. "Inheritance of Convexity for the Pmin-Restricted Game," Documents de travail du Centre d'Economie de la Sorbonne 17051, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Alexandre Skoda, 2017. "Inheritance of Convexity for the P min-Restricted Game," Post-Print halshs-01660670, HAL.
    3. Alexandre Skoda, 2016. "Complexity of inheritance of F-convexity for restricted games induced by minimum partitions," Post-Print halshs-01382502, HAL.
    4. Alexandre Skoda, 2016. "Complexity of inheritance of F-convexity for restricted games induced by minimum partitions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01382502, HAL.
    5. Alexandre Skoda, 2017. "Inheritance of Convexity for the P min-Restricted Game," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01660670, HAL.
    6. Alexandre Skoda, 2016. "Complexity of inheritance of F-convexity for restricted games induced by minimum partitions," Documents de travail du Centre d'Economie de la Sorbonne 16055, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

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    Keywords

    restricted game; partitions; communication networks; cooperative game;
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