IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v38y2021i05ns0217595921400066.html
   My bibliography  Save this article

A Combinatorial Characterization for Population Monotonic Allocations in Convex Independent Set Games

Author

Listed:
  • Bin Liu

    (School of Mathematical Sciences, Ocean University of China, Qingdao, P. R. China)

  • Han Xiao

    (School of Mathematical Sciences, Ocean University of China, Qingdao, P. R. China)

  • Qizhi Fang

    (School of Mathematical Sciences, Ocean University of China, Qingdao, P. R. China)

Abstract

Independent set games are cooperative games defined on graphs, where players are edges and the value of a coalition is the maximum size of independent sets in the subgraph defined by the coalition. In this paper, we study population monotonic allocation schemes for independent set games. For independent set games introduced by Deng et al. [X. Deng, T. Ibaraki and H. Nagamochi (1999). Algorithmic aspects of the core of combinatorial optimization games. Mathematics of Operations Research, 24(3), 751–766], we provide a combinatorial characterization for population monotonic allocation schemes in convex instances. For independent set games introduced by Xiao et al. [H. Xiao, Y. Wang and Q. Fang (2021). On the convexity of independent set games. Discrete Applied Mathematics, 291, 271–276], we prove the equivalence of convexity, population monotonicity and balancedness.

Suggested Citation

  • Bin Liu & Han Xiao & Qizhi Fang, 2021. "A Combinatorial Characterization for Population Monotonic Allocations in Convex Independent Set Games," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 38(05), pages 1-9, October.
    • Handle: RePEc:wsi:apjorx:v:38:y:2021:i:05:n:s0217595921400066
    DOI: 10.1142/S0217595921400066
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0217595921400066
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0217595921400066?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:wsi:apjorx:v:38:y:2021:i:05:n:s0217595921400066. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/apjor/apjor.shtml .

    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.