Convex game

[GeorgeR227]

Upon further reading, I've discovered the concept of a convex game which is even stronger than a super-additive game. A convex game must fulfill that v(S U T) >= v(S) + v(T) - v(S /\ T) while super-additive must only accomplish v(S U T) >= v(S) + v(T).

Apparently if we fulfill the convex game conditions, then we automatically get:

• A nonempty core
• The Shapley value included in the core

Our current example is not actually convex, since v(A,B,C) = 900 < v(A,B) + v(A,C) - v(A) = 600 + 600 - 0 = 1200, but perhaps we can formulate the general model to fit this?

[GeorgeR227]

Apparently, finding extreme points (vertices of the core) is polynomial, although there will probably be an exponential number of extreme points in the core.