Dependency in Cooperative Boolean Games

Cooperative boolean games are coalitional games with both goals and costs associated to actions, and dependence networks for boolean games are a kind of social networks representing how the actions of other agents have an influence on the achievement of an agent’s goal. In this paper, we introduce two new types of dependence networks, called the abstract dependence network and the refined dependence network. Moreover, we show that the notion of stability is complete with respect to the solution concept of the core in the case of cooperative boolean games with costly actions. We present a reduction, called Δ-reduction, to pass from a cooperative boolean game G to game G′ without loosing solutions.