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The socially stable core in structured transferable utility games

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  • Herings, P.J.J.

    (Tilburg University)

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

    (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, for instance a hierarchical ordering or a dominance relation.The social structure is utilized to refine the core of the game, being the set of payoffs to the players that cannot be improved upon by any coalition of players.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 of the game consists of the core elements that are socially stable.In case the social structure is such that every player in a coalition has the same power, social stability reduces to balancedness and the socially stable core coincides with 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 Tilburg University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-195976.

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Date of creation: 2007
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Publication status: Published in Games and Economic Behavior (2007) v.59, p.85-104
Handle: RePEc:ner:tilbur:urn:nbn:nl:ui:12-195976

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Web page: http://www.tilburguniversity.edu/

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  1. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-64, July.
  2. Ambec, Stefan & Sprumont, Yves, 2000. "Sharing a River," Cahiers de recherche 0006, GREEN.
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  8. Matthew O. Jackson & Asher Wolinsky, 1994. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Fernández, C. & Borm, P.E.M. & Hendrickx, R.L.P. & Tijs, S.H., 2002. "Drop Out Monotonic Rules for Sequencing Situations," Discussion Paper 2002-51, Tilburg University, Center for Economic Research.
  10. Gabrielle Demange, 2004. "On group stability in hierarchies and networks," Post-Print halshs-00581662, HAL.
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  12. René van den Brink & Gerard van der Laan & Valeri Vasil'ev, 2007. "Distributing Dividends in Games with Ordered Players," Tinbergen Institute Discussion Papers 06-114/1, Tinbergen Institute.
  13. Demange, Gabrielle, 1994. "Intermediate preferences and stable coalition structures," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 45-58, January.
  14. Herings, P.J.J. & Laan, G. van der & Talman, A.J.J., 2003. "Socially Structured Games and their Applications," Discussion Paper 2003-40, Tilburg University, Center for Economic Research.
  15. P. Herings & Gerard Laan & Dolf Talman, 2005. "The positional power of nodes in digraphs," Social Choice and Welfare, Springer, vol. 24(3), pages 439-454, 06.
  16. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
  17. Kalai, Ehud & Postlewaite, Andrew & Roberts, John, 1978. "Barriers to trade and disadvantageous middlemen: Nonmonotonicity of the core," Journal of Economic Theory, Elsevier, vol. 19(1), pages 200-209, October.
  18. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, vol. 12(1), pages 113-126, January.
  19. Roger B. Myerson, 1976. "Graphs and Cooperation in Games," Discussion Papers 246, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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Cited by:
  1. repec:dgr:uvatin:2010096 is not listed on IDEAS
  2. Erik Ansink & Hans-Peter Weikard, 2009. "Sequential Sharing Rules for River Sharing Problems," Working Papers 2009.114, Fondazione Eni Enrico Mattei.
  3. 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.
  4. repec:dgr:uvatin:2012006 is not listed on IDEAS
  5. 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 10-096/1, Tinbergen Institute.

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