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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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Bonnisseau, Jean-Marc & Iehle, Vincent, 2007. "Payoff-dependent balancedness and cores," Games and Economic Behavior, Elsevier, vol. 61(1), pages 1-26, October.
    2. 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.
    3. 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.
    4. 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.
    5. repec:dau:papers:123456789/89 is not listed on IDEAS
    6. Carvalho, M., 2011. "Essays in behavioral microeconomic theory," Other publications TiSEM 97fbb10e-5f12-420b-b8c4-e, Tilburg University, School of Economics and Management.
    7. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, March.
    8. repec:ebl:ecbull:v:3:y:2004:i:42:p:1-10 is not listed on IDEAS
    9. 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.
    10. Yan-An Hwang, 2013. "A note on the core," Journal of Global Optimization, Springer, vol. 55(3), pages 627-632, March.
    11. 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).
    12. 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.
    13. 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.

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    JEL classification:

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

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