Abstract: In this paper, the Banzhaf functions for static and dynamic cooperative games on matroids are discussed, which associate the description of the Shapley functions for these two kinds of matroids in papers[1, 2]. The existence and uniqueness of the Banzhaf functions for these two kinds of matroids are studied by the corresponding axiomatic systems, which expand the studying scope of the payoff indicators on matroids. Mean white, some properties are researched. Finally, a numerical example is given to illustrate the players’ Banzhaf payoffs on these two kinds of cooperative games.

Key words: cooperative games, Banzhaf function, matroids, basic coalitions, feasible coalitions

摘要： 本文结合文[1,2]中关于拟阵上静态结构和动态结构合作对策Shapley函数的描述,探讨了两类拟阵上的Banzhaf函数。通过给出相应的公理体系,论述了两类拟阵上Banzhaf函数的存在性和唯一性,拓展了拟阵上分配指标的研究范围。同时讨论了两类合作对策上Banzhaf函数的有关性质。最后通过算例来说明局中人在此类合作对策中的Banzhaf指标。

关键词: 合作对策, Banzhaf函数, 拟阵, 基联盟, 可行联盟