IDEAS home Printed from https://ideas.repec.org/p/tiu/tiutis/c2546c5b-249a-44a8-b917-7a36c78e276c.html
   My bibliography  Save this paper

Socially structured games

Author

Listed:
  • Herings, P.J.J.

    (Tilburg University, School of Economics and Management)

  • van der Laan, G.
  • Talman, A.J.J.

    (Tilburg University, School of Economics and Management)

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
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2007. "Socially structured games," Other publications TiSEM c2546c5b-249a-44a8-b917-7, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:c2546c5b-249a-44a8-b917-7a36c78e276c
    as

    Download full text from publisher

    File URL: https://pure.uvt.nl/ws/portalfiles/portal/796272/fulltext.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 128-154, April.
    2. 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.
    3. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Bollen, P.W.L., 2002. "A formal ORM-to -UML mapping algorithm," Research Memorandum 016, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    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. van den Brink, René & van der Laan, Gerard & Moes, Nigel, 2012. "Fair agreements for sharing international rivers with multiple springs and externalities," Journal of Environmental Economics and Management, Elsevier, vol. 63(3), pages 388-403.
    3. Sylvain Béal & Amandine Ghintran & Eric Rémila & Philippe Solal, 2015. "The sequential equal surplus division for rooted forest games and an application to sharing a river with bifurcations," Theory and Decision, Springer, vol. 79(2), pages 251-283, September.
    4. Carvalho, M., 2011. "Essays in behavioral microeconomic theory," Other publications TiSEM 97fbb10e-5f12-420b-b8c4-e, Tilburg University, School of Economics and Management.
    5. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, December.
    6. Yan-An Hwang, 2013. "A note on the core," Journal of Global Optimization, Springer, vol. 55(3), pages 627-632, March.
    7. Gudmundsson, Jens & Hougaard, Jens Leth & Ko, Chiu Yu, 2019. "Decentralized mechanisms for river sharing," Journal of Environmental Economics and Management, Elsevier, vol. 94(C), pages 67-81.
    8. Bonnisseau, Jean-Marc & Iehle, Vincent, 2007. "Payoff-dependent balancedness and cores," Games and Economic Behavior, Elsevier, vol. 61(1), pages 1-26, October.
    9. repec:dau:papers:123456789/89 is not listed on IDEAS
    10. repec:ebl:ecbull:v:3:y:2004:i:42:p:1-10 is not listed on IDEAS
    11. 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.
    12. 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).
    13. Gerard van der Laan & Nigel Moes, 2012. "Transboundary Externalities and Property Rights: An International River Pollution Model," Tinbergen Institute Discussion Papers 12-006/1, Tinbergen Institute.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2003. "Socially Structured Games and their Applications," Other publications TiSEM 271c701e-4489-41b3-8d9e-f, Tilburg University, School of Economics and Management.
    2. P. Herings & A. Predtetchinski & A. Perea, 2006. "The Weak Sequential Core for Two-Period Economies," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 55-65, April.
    3. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2000. "Cooperative Games in Graph Structure," Discussion Paper 2000-90, Tilburg University, Center for Economic Research.
    4. Kamijo, Yoshio, 2009. "A linear proportional effort allocation rule," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 341-353, November.
    5. C. Manuel & D. Martín, 2021. "A value for communication situations with players having different bargaining abilities," Annals of Operations Research, Springer, vol. 301(1), pages 161-182, June.
    6. Swapnil Dhamal & Y. Narahari, 2015. "Formation of Stable Strategic Networks with Desired Topologies," Studies in Microeconomics, , vol. 3(2), pages 158-213, December.
    7. Caulier, Jean-François & Mauleon, Ana & Vannetelbosch, Vincent, 2015. "Allocation rules for coalitional network games," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 80-88.
    8. Joss Sánchez-Pérez, 2019. "Solutions for network games and symmetric group representations," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(4), pages 95-123.
    9. Navarro, Noemí, 2010. "Flexible network rules for identified externalities," Games and Economic Behavior, Elsevier, vol. 69(2), pages 401-410, July.
    10. Herings, P. Jean-Jacques & van der Laan, Gerard & Talman, Dolf, 2007. "The socially stable core in structured transferable utility games," Games and Economic Behavior, Elsevier, vol. 59(1), pages 85-104, April.
    11. Surajit Borkotokey & Sujata Goala & Niharika Kakoty & Parishmita Boruah, 2022. "The component-wise egalitarian Myerson value for Network Games," Papers 2201.02793, arXiv.org.
    12. Borkotokey, Surajit & Chakrabarti, Subhadip & Gilles, Robert P. & Gogoi, Loyimee & Kumar, Rajnish, 2021. "Probabilistic network values," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 169-180.
    13. 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.
    14. Pin, Paolo, 2011. "Eight degrees of separation," Research in Economics, Elsevier, vol. 65(3), pages 259-270, September.
    15. Slikker, Marco, 2007. "Bidding for surplus in network allocation problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 493-511, November.
    16. Joost Vandenbossche & Thomas Demuynck, 2013. "Network Formation with Heterogeneous Agents and Absolute Friction," Computational Economics, Springer;Society for Computational Economics, vol. 42(1), pages 23-45, June.
    17. Jackson, Matthew O. & Zenou, Yves, 2015. "Games on Networks," Handbook of Game Theory with Economic Applications,, Elsevier.
    18. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Discounted Tree Solutions," Working Papers hal-01377923, HAL.
    19. Carayol, Nicolas & Delille, Rémy & Vannetelbosch, Vincent, 2015. "Allocating value among farsighted players in network formation," Economics Letters, Elsevier, vol. 137(C), pages 50-53.
    20. Newton, Jonathan, 2012. "Coalitional stochastic stability," Games and Economic Behavior, Elsevier, vol. 75(2), pages 842-854.

    More about this item

    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:tiu:tiutis:c2546c5b-249a-44a8-b917-7a36c78e276c. 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.

    If CitEc recognized a bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Richard Broekman (email available below). General contact details of provider: https://www.tilburguniversity.edu/about/schools/economics-and-management/ .

    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.