IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-01487381.html
   My bibliography  Save this paper

Inheritance of convexity for partition restricted games

Author

Listed:
  • Alexandre Skoda

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

Abstract

A correspondence P associates to every subset A ⊆ N a partition P ( A ) of A and to every game ( N , v ) , the P -restricted game ( N , v ¯ ) defined by v ¯ ( A ) = ∑ F ∈ P ( A ) v ( F ) for all A ⊆ N . We give necessary and sufficient conditions on P to have inheritance of convexity from ( N , v ) to ( N , v ¯ ) . The main condition is a cyclic intersecting sequence free condition. As a consequence, we only need to verify inheritance of convexity for unanimity games and for the small class of extremal convex games ( N , v S ) (for any 0̸ ≠ S ⊆ N ) defined for any A ⊆ N by v S ( A ) = | A ∩ S | − 1 if A ∩ S ≠ 0̸ , and v S ( A ) = 0 otherwise. In particular, when ( N , v ¯ ) corresponds to Myerson's network-restricted game, inheritance of convexity can be verified by this way. For the P min correspondence ( P min ( A ) is built by deleting edges of minimum weight in the subgraph G A of a weighted communication graph G ), we show that inheritance of convexity for unanimity games already implies inheritance of convexity

Suggested Citation

  • Alexandre Skoda, 2017. "Inheritance of convexity for partition restricted games," Post-Print halshs-01487381, HAL.
  • Handle: RePEc:hal:journl:halshs-01487381
    DOI: 10.1016/j.disopt.2017.01.004
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Alexandre Skoda, 2017. "Convexity of Graph-Restricted Games Induced by Minimum Partitions," Post-Print halshs-01659804, HAL.
    3. Alexandre Skoda, 2020. "Inheritance of Convexity for the P˜min-Restricted Game," Post-Print halshs-02967120, HAL.
    4. Alexandre Skoda, 2017. "Convexity of Graph-Restricted Games Induced by Minimum Partitions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01659804, HAL.
    5. Alexandre Skoda, 2020. "Inheritance of Convexity for the P˜min-Restricted Game," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02967120, HAL.
    6. A. Skoda, 2021. "Inheritance of convexity for the $$\mathcal {P}_{\min }$$ P min -restricted game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(1), pages 1-32, February.
    7. Alexandre Skoda, 2019. "Convexity of graph-restricted games induced by minimum partitions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01617023, HAL.
    8. 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.
    9. Alexandre Skoda, 2019. "Convexity of graph-restricted games induced by minimum partitions," Post-Print halshs-01617023, HAL.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:halshs-01487381. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.