Evaluating power of agents from dependence relations in boolean games

In this paper we propose a new methodology for evaluating the relative power of agents in a strategic situation formally represented by a boolean game. The methodology consists in extracting a power ranking from the dependence relation induced by a certain boolean game. Our approach is axiomatic. We provide a number of desirable postulates that a notion of dependence is expected to satisfy and we compare competing notions of dependence, included a notion based on the concept of veto player, with respect to them. Similarly, we provide a set of postulates for power functions (i.e., the family of functions mapping dependence graphs to power rankings) and evaluate some new methods as well as existing ones (e.g., Pagerank) with respect to this set of postulates.