On the coincidence property

The collection of the coalitions b is balanced if the Shapley value of the simple game χb is 0. This observation makes us able to derive a class of simple games with the coincidence property, that is, the Shapley value and the nucleolus coincide. And then we use such a class of simple games as generators to construct coincidence regions, convex cones consisting of games with the coincidence property. We will first propose the SP region. Two sets of games satisfying the coincidence property are introduced. Both are SP regions. In fact, the SP regions do not cover all games satisfying the coincidence property even for 3-person case. To enlarge the class of games with the coincidence property, the ST regions are proposed. All 3-person games with the coincidence property can be classified into 4 ST regions.