Compact Representations and Approximations for Compuation in Games

Compact representations have recently been developed as a way of both encoding the strategic interactions of a game in an intuitive way. They are also useful in speeding up the computation of important solution concepts such as Nash Equiliria, because they can often be represented in a size that is polynomial in the number of players. Rather than di- rectly encoding a game in a compact form, another approach is to factor the game into smaller subgames, and then perform computation in the factored space. In this paper, I give an overview of one kind of compact representation called a Graphical Game, and I discuss the approach of factoring games. I then use the idea of creating approximate factorings, which preserve ǫ-equilbria to develop a new algorithm that can be used to simplify computation in a Graphical Game by creating an approximate version.