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Games induced by the partitioning of a graph

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  • M. Grabisch
  • A. Skoda

Abstract

The paper aims at generalizing the notion of restricted game on a communication graph, introduced by Myerson. We consider communication graphs with weighted edges, and we define arbitrary ways of partitioning any subset of a graph, which we call correspondences. A particularly useful way to partition a graph is obtained by computing the strength of the graph. The strength of a graph is a measure introduced in graph theory to evaluate the resistance of networks under attacks, and it provides a natural partition of the graph (called the Gusfield correspondence) into resistant components. We perform a general study of the inheritance of superadditivity and convexity for the restricted game associated with a given correspondence. Our main result is to give for cycle-free graphs necessary and sufficient conditions for the inheritance of convexity of the restricted game associated with the Gusfield correspondence. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:201:y:2012:i:1:p:229-249:10.1007/s10479-012-1200-8
    DOI: 10.1007/s10479-012-1200-8
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    1. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    2. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.
    3. 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.
    4. 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.
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    Cited by:

    1. Alexandre Skoda, 2016. "Inheritance of Convexity for Partition Restricted Games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01318105, HAL.
    2. Alexandre Skoda, 2016. "Convexity of Network Restricted Games Induced by Minimum Partitions," Documents de travail du Centre d'Economie de la Sorbonne 16019, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Alexandre Skoda, 2017. "Convexity of Graph-Restricted Games Induced by Minimum Partitions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01659804, HAL.
    4. Alexandre Skoda, 2016. "Inheritance of Convexity for Partition Restricted," Documents de travail du Centre d'Economie de la Sorbonne 16040, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Alexandre Skoda, 2019. "Convexity of graph-restricted games induced by minimum partitions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01617023, HAL.
    6. Ata Atay & Marina Núñez, 2019. "Multi-sided assignment games on m-partite graphs," Annals of Operations Research, Springer, vol. 279(1), pages 271-290, August.
    7. 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.
    8. Alexandre Skoda, 2016. "Convexity of Network Restricted Games Induced by Minimum Partitions," Post-Print hal-01305005, HAL.
    9. Alexandre Skoda, 2016. "Convexity of Network Restricted Games Induced by Minimum Partitions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01305005, HAL.
    10. Alexandre Skoda, 2017. "Inheritance of Convexity for the P min-Restricted Game," Post-Print halshs-01660670, HAL.
    11. Alexandre Skoda, 2017. "Convexity of Graph-Restricted Games Induced by Minimum Partitions," Documents de travail du Centre d'Economie de la Sorbonne 17049, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    12. Alexandre Skoda, 2016. "Complexity of inheritance of F-convexity for restricted games induced by minimum partitions," Post-Print halshs-01382502, HAL.
    13. Alexandre Skoda, 2017. "Convexity of Graph-Restricted Games Induced by Minimum Partitions," Post-Print halshs-01659804, HAL.
    14. Alexandre Skoda, 2020. "Inheritance of Convexity for the P˜min-Restricted Game," Post-Print halshs-02967120, HAL.
    15. Alexandre Skoda, 2016. "Inheritance of Convexity for Partition Restricted Games," Post-Print halshs-01318105, HAL.
    16. Alexandre Skoda, 2020. "Inheritance of Convexity for the P˜min-Restricted Game," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02967120, HAL.
    17. Jerome Galtier, 2018. "Fast approximation of matroid packing and covering," Annals of Operations Research, Springer, vol. 271(2), pages 575-598, December.
    18. 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.
    19. Alexandre Skoda, 2020. "Inheritance of Convexity for the P˜min-Restricted Game," Documents de travail du Centre d'Economie de la Sorbonne 20020, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    20. Alexandre Skoda, 2017. "Inheritance of Convexity for the P min-Restricted Game," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01660670, HAL.
    21. Alexandre Skoda, 2019. "Convexity of graph-restricted games induced by minimum partitions," Post-Print halshs-01617023, HAL.
    22. 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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