具有区间支付的合作对策的区间Shapley值

Interval Shapley Value for Cooperative Games with Interval Payoffs

针对合作对策中支付函数是区间数的情形,利用区间数运算的性质,对Shapley值在经典意义下的三条公理进行拓广,并论证了该形式下的Shapley函数的唯一形式,并将区间Shapley值方法应用到供应链协调利益分配的实例中。由于支付函数是区间数,本文最终给出的分配的结果也是一个区间数。通过证明可知,由各个联盟对应区间支付范围内的不同实数值所组成的对策是经典合作对策,并且其Shapley值一定包含在区间Shapley值中。

In this paper,we make a study of the Shapley value with characteristic functions from the viewpoint that the payoff of each coalition are often only imprecisely or ambiguously known to the players as an interval number.Axioms of Shapley value which was given by Shapley in 1953 have been extended for the interval Shapley value.The explicit and exclusive interval Shapley value has been put forward,which has been applied to profit allocation scheme among partners in supply-chain.Because of the interval payoffs,the results of imputation in this paper are also interval numbers.Moreover,it is proven that any crisp Shapley value that corresponds to a real number belonging to interval range remains with the bound of interval Shapley.