Dependence in games and dependence games

In the multi-agent systems community, dependence theory and game theory are often presented as two alternative perspectives on the analysis of agent interaction. The paper presents a formal analysis of a notion of dependence between players, given in terms of standard game-theoretic notions of rationality such as dominant strategy and best response. This brings the notion of dependence within the realm of game theory providing it with the sort of mathematical foundations which still lacks. Concretely, the paper presents two results: first, it shows how the proposed notion of dependence allows for an elegant characterization of a property of reciprocity for outcomes in strategic games; and second, it shows how the notion can be used to define new classes of coalitional games, where coalitions can force outcomes only in the presence of reciprocal dependencies.