International Journal of Game Theory

, Volume 1, Issue 1, pp 11–26

Cores of convex games

  • Lloyd S. Shapley

DOI: 10.1007/BF01753431

Cite this article as:
Shapley, L.S. Int J Game Theory (1971) 1: 11. doi:10.1007/BF01753431


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.

Copyright information

© Physica-Verlag 1971

Authors and Affiliations

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