To deal with exponential growth in the size of a game with the number of agents, we propose an approximation based on a hierarchy of reduced games. The reduced game achieves sav-ings by restricting the number of agents playing any strategy to fixed multiples. We validate the idea through experiments on randomly generated local-effect games. An extended ap-plication to strategic reasoning about a complex trading sce-nario motivates the approach, and demonstrates methods for game-theoretic reasoning over incompletely-specified games at multiple levels of granularity
