Cooperative games under augmenting systems

Abstract. The goal of this paper is to develop a theoretical framework inorder to analyze cooperative games inwhich only certaincoalitions are allowed to form. We will axiomatize the structure of such allowable coalitions using the theory of antimatroids, a notion developed for combinatorially abstract sets. There have been previous models developed to confront the problem of unallowable coalitions. Games restricted by a communication graph were introduced by Myerson and Owen. We introduce a new combinatorial structure called augmenting system, which is a generalization of the antimatroid structure and the system of connected subgraphs of a graph. The main result of the paper is a direct formula of Shapley and Banzhaf values for games under augmenting systems restrictions