信息不完全下联盟结构合作对策的比例Owen解

Proportional Owen value for the coalition structure cooperative game under the incomplete information

不完全信息下联盟结构合作对策(简称不完全信息对策)是指特征函数中部分联盟价值缺失的联盟结构合作对策.Owen值应用前提是可行联盟的特征函数完全已知,因此Owen值不适用于求解不完全信息对策.根据不完全信息对策中已知可行联盟的特征函数,定义了比例Owen值.比例Owen值按照“二步法”对合作收益值进行两个层次的分配:一是优先联盟之间,二是优先联盟内部.与Owen值不同的是,在优先联盟内部比例Owen值依据每个成员对所在优先联盟的贡献率切割优先联盟的所得收益.比例Owen值满足一定的个体理性,并且通过公理化证明可知:比例Owen值是满足有效性、线性、零元联盟性和比例性等性质的唯一解,具有一定优良的性质.最后,将比例Owen值应用到一带一路背景下供应链中局中人作为整体参与合作的问题中,作为不完全信息下多层次合作的一种分配方案.

The incomplete information cooperative game is a kind of cooperative games with unknown characteristic value for some coaltion values.Because the Owen value is used to solve the coalition structure cooperative game under the totally complete information,the cooperation model under the above incomplete information(partially-defined cooperative game)has been unable to apply.In order to solve the partially-defined cooperative game,we defined proportional Owen value.The proportional Owen value is defined on the coalition with known value.Moreover,the total value of big coalition is allocated by two steps,i.e.,between an a prior coalition and in a single a prior coalition.The proportional Owen value is different from Owen value,because the allocation rate for the player in a single coalition is based on the contribution rate in their small coalition.The proportional Owen value satisfied individual rationality,and it is a unique value for partially-defined cooperative game satisfying efficiency,linearity,null coalition property and proportionality,and so on.Finally,the proportional Owen value is applied to the supply chain with some players as a whole under the background of one Belt and Road,as an allocation method for the multilevel cooperative problem with incomplete information.