IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v62y2007i1p1-29.html
   My bibliography  Save this article

Socially Structured Games

Author

Listed:
  • P. Herings

    ()

  • Gerard Laan

    ()

  • Dolf Talman

    ()

Abstract

We generalize the concept of a cooperative non-transferable utility game by introducing a socially structured game. In a socially structured game every coalition of players can organize themselves according to one or more internal organizations to generate payoffs. Each admissible internal organization on a coalition yields a set of payoffs attainable by the members of this coalition. The strengths of the players within an internal organization depend on the structure of the internal organization and are represented by an exogenously given power vector. More powerful players have the power to take away payoffs of the less powerful players as long as those latter players are not able to guarantee their payoffs by forming a different internal organization within some coalition in which they have more power. We introduce the socially stable core as a solution concept that contains those payoffs that are both stable in an economic sense, i.e., belong to the core of the underlying cooperative game, and stable in a social sense, i.e., payoffs are sustained by a collection of internal organizations of coalitions for which power is distributed over all players in a balanced way. The socially stable core is a subset and therefore a refinement of the core. We show by means of examples that in many cases the socially stable core is a very small subset of the core. We will state conditions for which the socially stable core is non-empty. In order to derive this result, we formulate a new intersection theorem that generalizes the KKMS intersection theorem. We also discuss the relationship between social stability and the wellknown concept of balancedness for NTU-games, a sufficient condition for non-emptiness of the core. In particular we give an example of a socially structured game that satisfies social stability and therefore has a non-empty core, but whose induced NTU-game does not satisfy balancedness in the general sense of Billera. Copyright Springer 2007

Suggested Citation

  • P. Herings & Gerard Laan & Dolf Talman, 2007. "Socially Structured Games," Theory and Decision, Springer, vol. 62(1), pages 1-29, February.
  • Handle: RePEc:kap:theord:v:62:y:2007:i:1:p:1-29
    DOI: 10.1007/s11238-006-9007-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11238-006-9007-1
    Download Restriction: Access to full text is restricted to subscribers.

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. van der Laan, G. & Talman, A.J.J. & Yang, Z., 1994. "Intersection theorems on polytopes," Discussion Paper 1994-20, Tilburg University, Center for Economic Research.
    2. P. Herings & Gerard Laan & Dolf Talman, 2005. "The positional power of nodes in digraphs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(3), pages 439-454, June.
    3. Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 128-154, April.
    4. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    5. P. Jean-Jacques Herings, 1997. "An extremely simple proof of the K-K-M-S Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(2), pages 361-367.
    6. Gerard van der Laan & Zaifu Yang & Dolf Talman, 1998. "Cooperative games in permutational structure," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 427-442.
    7. Nowak Andrzej S. & Radzik Tadeusz, 1994. "The Shapley Value for n-Person Games in Generalized Characteristic Function Form," Games and Economic Behavior, Elsevier, vol. 6(1), pages 150-161, January.
    8. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Erik Ansink & Hans-Peter Weikard, 2012. "Sequential sharing rules for river sharing problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 187-210, February.
    2. repec:dau:papers:123456789/89 is not listed on IDEAS
    3. repec:ebl:ecbull:v:3:y:2004:i:42:p:1-10 is not listed on IDEAS
    4. Lanzi, Diego, 2013. "Frames and social games," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 45(C), pages 227-233.
    5. Yan-An Hwang, 2013. "A note on the core," Journal of Global Optimization, Springer, vol. 55(3), pages 627-632, March.
    6. Jean-Marc Bonnisseau & Vincent Iehlé, 2007. "Payoff-dependent balancedness and cores (revised version)," UFAE and IAE Working Papers 678.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    7. Bonnisseau, Jean-Marc & Iehle, Vincent, 2007. "Payoff-dependent balancedness and cores," Games and Economic Behavior, Elsevier, vol. 61(1), pages 1-26, October.

    More about this item

    Keywords

    balancedness; core; non-transferable utility game; social stability; C71;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

    Statistics

    Access and download statistics

    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:kap:theord:v:62:y:2007:i:1:p:1-29. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: http://www.springer.com .

    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.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.