A Survey on the Computation of Power Indices

A ‘power index’ is a concept in cooperative game theory. Power indices are used as a measure for the influence that a player has in a certain class of cooperative games called simple games. As the title says, this is a survey on how to compute these power indices. Generally speaking, computing these indices is a tedious task, even for relatively small cooperative games. It is certainly intractable to do this by hand, and therefore as you might have guessed, we need computers to do this for us. In this survey we give first a short introduction to cooperative game theory with a focus on simple games. We discuss the power indices that have been proposed in the literature, and we present algorithms for computing some of these indices. The majority of the algorithms for computing power indices that have been proposed are suited for weighted voting games: an important subclass of simple games. Therefore, the majority of the algorithms that we present here are only suited for weighted voting games. Among the algorithms that we discuss are some of the best that are currently known. In the last chapter, we give some interesting directions for future research. Throughout our survey we try to pay special attention to the relation between computing power indices, computational complexity (one chapter is dedicated to this) and approximability.