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Prosperity properties of TU-games

Author

Listed:
  • 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.

Suggested Citation

  • J. R. G. van Gellekom & J. A. M. Potters & J. H. Reijnierse, 1999. "Prosperity properties of TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 211-227.
  • 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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    References listed on IDEAS

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    1. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, pages 89-99.
    2. Andrzej S. Nowak, 1997. "note: On an Axiomatization of the Banzhaf Value without the Additivity Axiom," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 137-141.
    3. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 261-281.
    4. Nowak, A.S. & Radzik, T., 1995. "On axiomatizations of the weighted Shapley values," Games and Economic Behavior, Elsevier, vol. 8(2), pages 389-405.
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    Citations

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    Cited by:

    1. Hans Koster & Jos van Ommeren & Piet Rietveld, 2011. "Geographic Concentration of Business Services Firms: A Poisson Sorting Model," ERSA conference papers ersa11p750, European Regional Science Association.
    2. Marina Núnez & Tamás Solymosi, 2014. "Lexicographic allocations and extreme core payoffs: the case of assignment games," IEHAS Discussion Papers 1425, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
    3. Shellshear, Evan & Sudhölter, Peter, 2009. "On core stability, vital coalitions, and extendability," Games and Economic Behavior, Elsevier, vol. 67(2), pages 633-644, November.
    4. Jesús Getán & Jesús Montes & Carles Rafels, 2014. "A note: characterizations of convex games by means of population monotonic allocation schemes," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 871-879, November.
    5. Dinko Dimitrov & Emiliya A. Lazarova & Shao-Chin Sung, 2016. "Inducing stability in hedonic games," University of East Anglia School of Economics Working Paper Series 2016-09, School of Economics, University of East Anglia, Norwich, UK..
    6. Calleja, Pedro & Rafels, Carles & Tijs, Stef, 2009. "The aggregate-monotonic core," Games and Economic Behavior, Elsevier, vol. 66(2), pages 742-748, July.
    7. Marina Núnez & Tamás Solymosi, 2014. "Lexicographic allocations and extreme core payoffs: the case of assignment games," IEHAS Discussion Papers 1425, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
    8. Pedro Calleja & Carles Rafels & Stef Tijs, 2006. "The Aggregate-Monotonic Core," Working Papers 280, Barcelona Graduate School of Economics.
    9. van Velzen, Bas & Hamers, Herbert & Solymosi, Tamas, 2008. "Core stability in chain-component additive games," Games and Economic Behavior, Elsevier, pages 116-139.
    10. Estévez-Fernández, Arantza, 2012. "New characterizations for largeness of the core," Games and Economic Behavior, Elsevier, vol. 76(1), pages 160-180.

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