A value for games on augmenting systems with a coalition structure

The purpose of this paper is to discuss games on augmenting systems with a coalition structure, where all feasible subsets of the coalition structure and that of each union both form an augmenting system. A value named the augmenting symmetric Banzhaf coalitional value is introduced. The distribution of power in the Basque Parliament emerging is provided to illustrate the concrete application of the value. Meanwhile, two axiomatic systems are established.