ABSTRACT
Many models have been developed to confront the problem of feasible coalitions. The first model in which the feasible coalitions are defined by the connected subgraphs of a graph is introduced by Myerson[7]. Contributions on graph-restricted games include Owen[8], Borm et al.[9], and Hamiache[10]. In these models, the possibilities of coalition formation are determined by a communication graph between the players. Another type of model introduced by Gilles et al.[11] and van den Brink[12] is equivalent to a subclass of antimatroids. In their model, the possibilities of coalition formation are determined by the positions of the players in a so-called permission structure. Faigle and Kern[13] proposed another model for cooperative games under precedence constraints, which are defined by games on a lattice of feasible subsets. Bilbao and Ordónez[14] introduced a combinatorial structure called “augmenting system,” which is a generalization of the antimatroid structure and the system of connected subgraphs of a graph. Sun and Zhang[15] studied the problem of profit allocation by introducing a lattice structure based on the situation that all the coalitions are not feasible, and they proposed the Owen value for games with coalition structures under precedence constraints, which will be called “restricted Owen value” for simplicity.
