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Prosperity properties of TU-games

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Author Info

  • J. R. G. van Gellekom

    ()
    (Department of Mathematics, University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands)

  • J. A. M. Potters

    ()
    (Department of Mathematics, University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands)

  • J. H. Reijnierse

    ()
    (Department of Mathematics, University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands)

Abstract

An important open problem in the theory of TU-games is to determine whether a game has a stable core (Von Neumann-Morgenstern solution (1944)). This seems to be a rather difficult combinatorial problem. There are many sufficient conditions for core-stability. Convexity is probably the best known of these properties. Other properties implying stability of the core are subconvexity and largeness of the core (two properties introduced by Sharkey (1982)) and a property that we have baptized extendability and is introduced by Kikuta and Shapley (1986). These last three properties have a feature in common: if we start with an arbitrary TU-game and increase only the value of the grand coalition, these properties arise at some moment and are kept if we go on with increasing the value of the grand coalition. We call such properties prosperity properties. In this paper we investigate the relations between several prosperity properties and their relation with core-stability. By counter examples we show that all the prosperity properties we consider are different.

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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 28 (1999)
Issue (Month): 2 ()
Pages: 211-227

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Handle: RePEc:spr:jogath:v:28:y:1999:i:2:p:211-227

Note: Received: June 1998/Revised version: December 1998
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Related research

Keywords: Stable core · large core · subconvexity · prosperity;

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Citations

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Cited by:
  1. Arantza Estevez-Fernandez, 2011. "New Characterizations for Largeness of the Core," Tinbergen Institute Discussion Papers 11-086/1, Tinbergen Institute.
  2. Shellshear, Evan & Sudhölter, Peter, 2009. "On core stability, vital coalitions, and extendability," Games and Economic Behavior, Elsevier, vol. 67(2), pages 633-644, November.
  3. Calleja, Pedro & Rafels, Carles & Tijs, Stef, 2009. "The aggregate-monotonic core," Games and Economic Behavior, Elsevier, vol. 66(2), pages 742-748, July.
  4. Arantza Estevez-Fernandez, 2011. "New Characterizations for Largeness of the Core," Tinbergen Institute Discussion Papers 11-086/1, Tinbergen Institute.
  5. Pedro Calleja & Carles Rafels & Stef Tijs, 2006. "The Aggregate-Monotonic Core," Working Papers 280, Barcelona Graduate School of Economics.
  6. Velzen, S. van & Hamers, H.J.M. & Solymosi, T., 2004. "Core Stability in Chain-Component Additive Games," Discussion Paper 2004-101, Tilburg University, Center for Economic Research.

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