A set game, in which the worth of a coalition is expressed by a set instead of a real number, is a new type of cooperative game. A F-restricted set game is a set game restricted by partition system. The main theorems show the structures of IM-value,OIM-value,SCM-value and ICM-value respectively,and the equivalency of IM value and the OIM-value for monotonic set games restricted by partition system as well.
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.
