Issued Under Office of Naval Research Contract No. Nonr 1858(16) CHARACTERIZATION OF THE KERNELS OF CONVEX GAMES

A convex game is characterized by increasing marginal utility for coalition membership as coalitions grow larger. The core of any n~person game is the set of outcomes that cannot be profitably blocked by any coalition. It is known that various solution concepts bear direct relation to the core when the game concerned is convex. Thus, the von Neumann-Morgens tern solution and the bargaining set c/T^ T^ coincide with the core and the value is essentially the ceni-er of gravity of the extreme points of the core (see [10],[6]). In this paper we consider another solution concept the kernel, and show that for convex games it is a unique point, thus it coincides with the nucleolus of the game (see [9]), and constitutes another distinguished point of the core different, in general, from the value. Roughly speaking, it is obtained by pushing inside at equal -t-.-distances certain supporting hyperplanes which determine the core, stopping the push of a hyperplane short of causing the inside to become void. 1 i \