This graphic, derived from a four person game, shows the imputation set
(triangle), the upper set (upside down triangle), and the core solution
that is in this case a full dimensional convex polyhedron. This is due to
the convexity of the game. The upper set coincides in this example with
the reasonable set. Inside of the core skeleton you can see the
kernel solution (enlarged red dot) that coincides with the nucleolus for
convex games. The yellow enlarged dot represents the Shapley value of the
game. Created by Holger Meinhardt (Holger.Meinhardt@wiwi.uni-karlsruhe.de).
For more information on game theory, see the
entry. A package for examining these systems is available in
This graphic, submitted by Holger Meinhardt, makes use of a
Mathematica add-on package called
and was rendered using POVRay. A third party library written by Komei
Fukuda was also used via MathLink to speed up the
computation of the vertices of the convex polyhedrons.