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Complexity of inheritance of F-convexity for 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

Let G = (N,E,w ) be a weighted communication graph (with weight function w on E ). For every subset A ⊆ N, we delete in the subset E (A ) of edges with ends in A, all edges of minimum weight in E (A ). Then the connected components of the corresponding induced subgraph constitue a partition of A that we Pmin(A ). For every game (N , v ), we define the Pmin-restricted game (N , v ) by v (A = ∑F∈ Pmin (A) v(F ) for all A ⊆ N. We prove that we can decide in polynomial time if there is inheritance of F-convexity from N , v ) to the Pmin-restricted game (N , v ) where F-convexity is obtained by restricting convexity to connected subsets

Suggested Citation

  • 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.
    • Handle: RePEc:hal:cesptp:halshs-01382502
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01382502
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. EDMONDS, Jack & GILES, Rick, 1977. "A min-max relation for submodular functions on graphs," LIDAM Reprints CORE 301, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. repec:hal:pseose:hal-00803233 is not listed on IDEAS
    5. 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.
    6. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    7. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.
    8. 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.
    9. 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.
    10. repec:hal:pseose:hal-00830291 is not listed on IDEAS
    11. Alexandre Skoda, 2016. "Convexity of Network Restricted Games Induced by Minimum Partitions," Post-Print hal-01305005, HAL.
    12. Alexandre Skoda, 2016. "Convexity of Network Restricted Games Induced by Minimum Partitions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01305005, HAL.
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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, 2019. "Convexity of graph-restricted games induced by minimum partitions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01617023, HAL.
    3. 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.
    4. 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.
    5. Alexandre Skoda, 2017. "Convexity of Graph-Restricted Games Induced by Minimum Partitions," Post-Print halshs-01659804, HAL.
    6. Alexandre Skoda, 2020. "Inheritance of Convexity for the P˜min-Restricted Game," Post-Print halshs-02967120, HAL.
    7. Alexandre Skoda, 2016. "Inheritance of Convexity for Partition Restricted Games," Post-Print halshs-01318105, HAL.
    8. Alexandre Skoda, 2019. "Convexity of graph-restricted games induced by minimum partitions," Post-Print halshs-01617023, HAL.
    9. Alexandre Skoda, 2017. "Convexity of Graph-Restricted Games Induced by Minimum Partitions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01659804, HAL.
    10. 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.
    11. Alexandre Skoda, 2020. "Inheritance of Convexity for the P˜min-Restricted Game," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02967120, HAL.

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    Keywords

    graph; complexity; supermodularity; partitions; communication networks; cooperative game; convex game; restricted game;
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