准许树博弈的权重准许分支公平和准许树限制核

Weighted permission component fairness and permission tree restricted core of permission tree games

准许树结构是对具有等级划分的组织结构的抽象.例如公司或团体的成员结构,只有上级准许的情况下下级成员才能执行某些活动.此外,在同一组织中下级成员间的合作往往多于竞争,但这种合作必须得到上级成员的许可才能进行.本文研究了具有准许树结构的博弈(即准许树博弈)的解.首先提出了权重准许分支公平公理,并由此得到了一个与权重系统相关的解,即权重准许值.其次,利用有效性,非本质元性质和权重准许分支公平这三个公理,对给定权重系统解的唯一性进行了完全刻画.最后,证明了当准许树博弈满足锥模性质时由权重系统集确定的解集与它的准许树限制核是等价的.

Permission tree is abstracted from the hierarchy structure of organizations, such as tim mem- bership of companies or parties. This structure indicates the relationship of permissions between members, where some one whom only be permitted by others can perform actions. However, cooperation is more important than competition in the same group, even though this kind of cooperation must be permit- ted. This paper investigates the solution of games with permission restricted and tree structures, shortly permission tree games. To obtain the new solution （i.e., weighted permission value）, weighted permission component fairness axiom is derived from the permission component fairness of the average tree pernfission value. With the new axiom and other two properties： the efficiency and the inessential player, the proposed solution relevant to the given weighted system is characterized. Finally, we show that the solutions set concerned the weighted systems coincides with the permission tree restricted core.