This paper proposes two new solution concepts for transferable utility coalitional games that are Core selections, the Central Core and the Mid-central Core, with the first being set-valued and the latter point-valued. The basic idea at the root of the Central Core is to allow such Core elements that grant to each player at least the pay-off obtained from the centroid of the extreme points of the Core of the same game but with the worth of the grand coalition reduced to the minimum value such that the game remains balanced. The Mid-central Core is defined as the centroid of the extreme points of the Central Core.

Some basic geometrical properties of the Central Core are then analysed, showing that it is a convex polytope that coincides with the Core under particular circumstances, or it is a strict subset of the Core. It is further shown that almost all fundamental axiomatic properties of the Core are preserved by these solutions.

Finally, an axiomatization of the Mid-central Core is provided through the adaptation of the mid-point domination property to a coalitional setting. The Mid-central Core is the only solution satisfying individual and group rationality together with aggregate monotonicity and a version of mid-point domination whose reference set is shaped according to the mentioned axioms.

本文针对可转移的效用联盟游戏提出了两个新的解决方案概念，即核心选择，中部核心和中部中部核心，第一个是集合值，后一个是点值。核心核心的基本思想是允许这样的核心元素至少向每个玩家授予从同一游戏核心极端点的质心获得的收益，但具有巨人联盟的价值降低到最小值，以使游戏保持平衡。中央核心的定义是中央核心的端点的质心。

然后分析了中央岩心的一些基本几何特性，表明它是一个凸多面体，在特定情况下与岩心重合，或者它是岩心的严格子集。进一步表明，这些解决方案保留了核心的几乎所有基本公理特性。

最后，中点核心的公理化是通过将中点控制权属性调整为联合环境来实现的。中央中枢是唯一满足个体和群体理性以及总体单调性和中点支配版本的解决方案，中点支配版本的参考集是根据上述公理确定的。