International Journal of Game Theory

, Volume 1, Issue 1, pp 11–26 | Cite as

Cores of convex games

  • Lloyd S. Shapley


The core of ann-person game is the set of feasible outcomes that cannot be improved upon by any coalition of players. A convex game is defined as one that is based on a convex set function. In this paper it is shown that the core of a convex game is not empty and that it has an especially regular structure. It is further shown that certain other cooperative solution concepts are related in a simple way to the core: The value of a convex game is the center of gravity of the extreme points of the core, and the von Neumann-Morgenstern stable set solution of a convex game is unique and coincides with the core.


Economic Theory Game Theory Extreme Point Solution Concept Regular Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Physica-Verlag 1971

Authors and Affiliations

  • Lloyd S. Shapley
    • 1
  1. 1.The Rand CorporationSanta Monica

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