IDEAS home Printed from
   My bibliography  Save this article

Hierarchical outcomes and collusion neutrality on networks


  • Park, Junghum
  • Ju, Biung-Ghi


We investigate TU-game solutions that are neutral to collusive agreements among players. A collusive agreement binds collusion members to act as a single player and is feasible when they are connected on a network. Collusion neutrality requires that no feasible collusive agreement can change the total payoff of collusion members. We show that on the domain of network games, there is a solution satisfying collusion neutrality, efficiency and null-player property if and only if the network is a tree. Considering a tree network, we show that affine combinations of hierarchical outcomes (Demange, 2004; van den Brink, 2012) are the only solutions satisfying the three axioms together with linearity. As corollaries, we establish characterizations of the average tree solution (equally weighted average of hierarchical outcomes); one established earlier in the literature and the others new.

Suggested Citation

  • Park, Junghum & Ju, Biung-Ghi, 2016. "Hierarchical outcomes and collusion neutrality on networks," European Journal of Operational Research, Elsevier, vol. 254(1), pages 179-187.
  • Handle: RePEc:eee:ejores:v:254:y:2016:i:1:p:179-187
    DOI: 10.1016/j.ejor.2016.03.011

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL:
    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.


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

    Cited by:

    1. László Á. Kóczy, 2022. "Core-stability over networks with widespread externalities," Annals of Operations Research, Springer, vol. 318(2), pages 1001-1027, November.
    2. Hui He & Lilong Zhu, 2020. "Online shopping green product quality supervision strategy with consumer feedback and collusion behavior," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-19, March.


    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:eee:ejores:v:254:y:2016:i:1:p:179-187. 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: Catherine Liu (email available below). General contact details of provider: .

    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.