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The Socially Stable Core in Structured Transferable Utility Games

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  • P. Jean-Jacques Herings

    ()
    (Dept of Economics and METEOR, Universiteit Maastricht)

  • Gerard van der Laan

    ()
    (Faculty of Economics and Econometrics, Vrije Universiteit Amsterdam)

  • Dolf Talman

    ()
    (Dept of Econometrics & Operations Research and CentER, Tilburg University)

Abstract

We consider cooperative games with transferable utility (TU-games), in which we allow for a social structure on the set of players. The social structure is utilized to refine the core of the game. For every coalition the relative strength of a player within that coalition is induced by the social structure and is measured by a power function. We call a payoff vector socially stable if at the collection of coalitions that can attain it, all players have the same power. The socially stable core is the set of socially stable elements of the core. We show that the socially stable core is non-empty if the game itself is socially stable. In general the socially stable core consists of a finite number of faces of the core and generically consists of a finite number of payoff vectors. Convex TU-games have a non-empty socially stable core, irrespective of the power function. When there is a clear hierarchy of players in terms of power, the socially stable core of a convex TU-game consists of exactly one element, an appropriately defined marginal vector. We demonstrate the usefulness of the concept of the socially stable core by two applications. One application concerns sequencing games and the other one the distribution of water.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 04-043/1.

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Date of creation: 23 Apr 2004
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Handle: RePEc:dgr:uvatin:20040043

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Web page: http://www.tinbergen.nl

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Keywords: Transferable Utility game; Social structure; Balancedness; Core;

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  1. Ambec, S. & Sprumont, Y., 2000. "Sharing a River," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 2000-08, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
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  15. Gilles, R.P. & Owen, G. & Brink, J.R. van den, 1991. "Games with permission structures: The conjunctive approach," Discussion Paper, Tilburg University, Center for Economic Research 1991-14, Tilburg University, Center for Economic Research.
  16. Fernández, C. & Borm, P.E.M. & Hendrickx, R.L.P. & Tijs, S.H., 2002. "Drop Out Monotonic Rules for Sequencing Situations," Discussion Paper, Tilburg University, Center for Economic Research 2002-51, Tilburg University, Center for Economic Research.
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Cited by:
  1. Erik Ansink & Hans-Peter Weikard, 2009. "Sequential Sharing Rules for River Sharing Problems," Working Papers, Fondazione Eni Enrico Mattei 2009.114, Fondazione Eni Enrico Mattei.
  2. Gerard van der Laan & Nigel Moes, 2012. "Transboundary Externalities and Property Rights: An International River Pollution Model," Tinbergen Institute Discussion Papers, Tinbergen Institute 12-006/1, Tinbergen Institute.
  3. Rene van den Brink & Gerard van der Laan & Nigel Moes, 2010. "Fair Agreements for Sharing International Rivers with Multiple Springs and Externalities," Tinbergen Institute Discussion Papers, Tinbergen Institute 10-096/1, Tinbergen Institute.
  4. Rene van den Brink & Gerard van der Laan & Nigel Moes, 2010. "Fair Agreements for Sharing International Rivers with Multiple Springs and Externalities," Tinbergen Institute Discussion Papers, Tinbergen Institute 10-096/1, Tinbergen Institute.
  5. Gerard van der Laan & Nigel Moes, 2012. "Transboundary Externalities and Property Rights: An International River Pollution Model," Tinbergen Institute Discussion Papers, Tinbergen Institute 12-006/1, Tinbergen Institute.

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