In this paper, we introduce several improved Shapley values for cooperative transferable utility (TU) games depending on the players’ least square contributions instead of their marginal contributions. This work is mainly enlightened by the Shapley value and the player’s productivity-based excess (usually called the excess of the player). Based on the player’s contribution-based excess, two quadratic programming models for obtaining the players’ (weighted) least square contributions are constructed. The efficient weighted Shapley-like value proposed in this paper as an extension of the Shapley value can be characterized by four independent axioms such as the symmetry, the efficiency, the additivity, and the quasi-null player, which are almost similar to the Shapley value’s four axioms except that the anonymity is replaced with the quasi-null player. The four axioms are proven to uniquely determine the efficient weighted Shapley-like value. Finally, the advantages of the proposed values are illustrated with a real case about the collaborative profit sharing of the rural e-commerce.

在本文中，我们为合作可转移效用（TU）游戏引入了几个改进的Shapley值，具体取决于玩家的最小二乘贡献而不是其边际贡献。Shapley值和玩家基于生产率的过剩（通常称为玩家过剩）对我们的工作起到了很大的启发作用。基于玩家贡献的超额，构造了两个二次规划模型来获得玩家（加权）最小二乘贡献。本文提出的有效加权类似Shapley的值是Shapley值的扩展，可以通过四个独立的公理来表征，例如对称性，效率，可加性和拟零参与者，它们几乎与Shapley值的四个公理相似，但匿名性被准零玩家取代了。事实证明，这四个公理可以唯一确定有效的加权Shapley样值。最后，通过有关农村电子商务协同收益共享的实际案例来说明所提出的价值的优势。