Game Theory

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 MathWorld entry. A package for examining these systems is available in the Mathematica Information Center.

This graphic, submitted by Holger Meinhardt, makes use of a Mathematica add-on package called MathGL3D 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.