拟阵限制下合作对策解的传递性

The Transfer Value for Games on Matroids

Vincent Feltkamp研究了Shapley解和Banzhaf解的公理性[3].Bilbao等人又对拟阵限制下的Shapley解的性质进行了讨论[1,2].本文在此基础上主要研究了拟阵限制下的合作对策Shapley解,并利用传递性、交换性、概率有效性和P-哑元性等四条公理证明了拟阵限制下合作对策Shapley解的唯一性.进而证明了拟阵限制条件下简单对策Shapley解的唯一性.最后给出了拟阵限制下合作对策的Banzhaf解的唯一性定理.

In a paper in 1995, Vincent Feltkamp characterized the Shapley and Banzhaf values. In 2001, Bilbao and Driessen characterized the Shapley value for games on matroids. This paper extends these characterizations to axiomatic characterizations of the Shapley and Banzhaf values for games on matroids. In particular, it is shown that the additivity axiom which is usually used to characterize these values can be weakened without changing the result.