一种基于Shapley值的联盟结构分配方法

A Method of Allocation Among Players in Coalition Structure Based on the Shapley Value

提出一种针对联盟结构博弈问题的新的收益分配方法.通过分析Owen联盟结构博弈模型的局限性,在最大联盟不确定形成及特征函数不确定满足超加性时,建立了二级联盟结构合作博弈模型.提出了可行联盟结构条件下局中人分配规则并证明了该分配规则的性质.新分配方法保障实现个体局中人局部理性与联盟结构集体理性,是联盟结构保持稳定的一个必要条件.通过算例分析,验证了该分配方案的有效性.

The aim of the paper is to seek a new method of profit allocation for games with coalition structure. By presenting the limitation of the model of Owen coalition structure, the model of two levels cooperative games with coalition structure is established when the grand coalition cannot be created and the characteristic functions are not supperadditive. The rule of allocation of feasible coalition structure is constructed and the relative properties are proved. The new rule of allocation guarantees the realization of both individual rationality and collective rationality and becomes a necessary condition to keep the coalition structure stable. The validity of the method is verified by a numerical example.