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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. Gabrielle Demange, 2004. "On Group Stability in Hierarchies and Networks," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 112(4), pages 754-778, August.
  2. Ambec, Stefan & Sprumont, Yves, 2000. "Sharing a River," Cahiers de recherche, GREEN 0006, GREEN.
  3. Roger B. Myerson, 1976. "Graphs and Cooperation in Games," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 246, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, Econometric Society, vol. 51(4), pages 1047-64, July.
  5. P. Herings & Gerard Laan & Dolf Talman, 2005. "The positional power of nodes in digraphs," Social Choice and Welfare, Springer, Springer, vol. 24(3), pages 439-454, 06.
  6. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, Elsevier, vol. 12(1), pages 113-126, January.
  7. Matthew O. Jackson & Asher Wolinsky, 1994. "A Strategic Model of Social and Economic Networks," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1098, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Cristina Fernández & Peter Borm & Ruud Hendrickx & Stef Tijs, 2005. "Drop out monotonic rules for sequencing situations," Computational Statistics, Springer, Springer, vol. 61(3), pages 501-504, 07.
  9. Le Breton,Michel & Owen,Guillermo & Weber,Shlomo, 1991. "Strongly balanced cooperative games," Discussion Paper Serie A, University of Bonn, Germany 338, University of Bonn, Germany.
  10. Herings, P.J.J. & Laan, G. van der & Talman, A.J.J., 2003. "Socially Structured Games and their Applications," Discussion Paper, Tilburg University, Center for Economic Research 2003-40, Tilburg University, Center for Economic Research.
  11. Mamoru Kaneko & Myrna Holtz Wooders, 1982. "Cores of Partitioning Games," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 620, Cowles Foundation for Research in Economics, Yale University.
  12. 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.
  13. Kalai, Ehud & Postlewaite, Andrew & Roberts, John, 1978. "Barriers to trade and disadvantageous middlemen: Nonmonotonicity of the core," Journal of Economic Theory, Elsevier, Elsevier, vol. 19(1), pages 200-209, October.
  14. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer, Springer, vol. 21(3), pages 249-66.
  15. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, Elsevier, vol. 25(2), pages 283-286, October.
  16. Demange, G., 1991. "Intermediate Preferences and Stable Coalition Structures," DELTA Working Papers, DELTA (Ecole normale supérieure) 91-16, DELTA (Ecole normale supérieure).
  17. Winter, Eyal, 1989. "A Value for Cooperative Games with Levels Structure of Cooperation," International Journal of Game Theory, Springer, Springer, vol. 18(2), pages 227-40.
  18. René van den Brink & Gerard van der Laan & Valeri Vasil'ev, 2007. "Distributing Dividends in Games with Ordered Players," Tinbergen Institute Discussion Papers, Tinbergen Institute 06-114/1, Tinbergen Institute.
  19. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Open Access publications from Tilburg University, Tilburg University urn:nbn:nl:ui:12-154855, Tilburg University.
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Cited by:
  1. 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.
  2. Erik Ansink & Hans-Peter Weikard, 2012. "Sequential sharing rules for river sharing problems," Social Choice and Welfare, Springer, Springer, vol. 38(2), pages 187-210, February.
  3. repec:dgr:uvatin:2010096 is not listed on IDEAS
  4. repec:dgr:uvatin:2012006 is not listed on IDEAS
  5. 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.

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