International Journal of Game Theory

, Volume 28, Issue 2, pp 211–227

Prosperity properties of TU-games

  • J. R. G. van Gellekom
  • J. A. M. Potters
  • J. H. Reijnierse

DOI: 10.1007/s001820050106

Cite this article as:
van Gellekom, J., Potters, J. & Reijnierse, J. Game Theory (1999) 28: 211. doi:10.1007/s001820050106

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.

Key words: Stable corelarge coresubconvexityprosperity

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • J. R. G. van Gellekom
    • 1
  • J. A. M. Potters
    • 1
  • J. H. Reijnierse
    • 1
  1. 1.Department of Mathematics, University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands (e-mail: gellekom@sci.kun.nl)NL