Hierarchical Decompositions of Stochastic Pursuit-Evasion Games

In this work we present a hierarchical framework for solving discrete stochastic pursuit-evasion games (PEGs) in large grid worlds. Given a partition of the grid world into superstates, the proposed approach creates a two-resolution decision-making process, which consists of a set of local PEGs at the original state level and an aggregated PEG at the superstate level. With much smaller state spaces, both the local games and the aggregated game can be easily solved to Nash equilibria. Through numerical simulations, we show that the proposed hierarchical framework significantly reduces the computation overhead, while still maintaining a satisfactory performance.