Novel equal division values based on players’ excess vectors and their applications to logistics enterprise coalitions

Abstract

Some sub-coalitions can not be formed or fail to satisfy the superadditivity in many realistic cooperative transferable utility (TU) games, which particularly exists in the logistics service industry. To exploit some novel solutions for addressing these TU games, we firstly propose again the equal surplus division value based on the least square method and players’ common excess vector, and then introduce the weighted equal surplus division value. Both of them belong to the family of the least square values. Inspired by the fact that many TU games base the profit distribution strategies not only on the egalitarian principle but also on the utility principle, the equal contribution division value and the weighted equal contribution division value based on the least square method and players’ contribution excess vector are spontaneously generated. An algorithm is described to make the four solutions proposed in this paper satisfy the property of individual rationality. Finally, to show the advantages, the practicability and the rationality of the four solutions, a practical example about the profit distribution strategy of a logistics enterprise coalition is illustrated and the contrastive analysis among them is given.