Abstraction in Large Extensive Games
Kevin Waugh · 2009
For zero-sum games, we have efficient solution techniques. Unfortunately, there are interesting games that are too large to solve. Here, a popular approach is to solve an abstract game that models the original game. We assume that more accurate the abstract games result in stronger strategies. There is substantial evidence to support this assumption. We begin by formalizing abstraction and refinement, a notion of expressive power for abstractions. We then show the assumption fails to hold under two criteria. The first is exploitability, which measures performance in the worst-case. The second is called the domination value, which measures how many mistakes a strategy makes. Despite these pathologies, we notice that larger strategies tend to make fewer mistakes and perform better in tournaments. Finally, we introduce strategy grafting, a technique that uses sub-game decomposition, which allow us to create good strategies in much larger spaces than previously possible.