Pursuit-evasion games have been studied as a generalization of many control problems, and have been also used to study the viability of running control algorithms over sensor networks. We provide a method for computing performance bounds on a sample pursuit-evasion game, the Classic Lifeline Game described by Rufus Isaacs. Given a routing topology and pairwise link probabilities, we compute an n-hop disk model abstraction of a sensor network to model delay and lost packets. Using this model, we then compute a probabilistic barrier that splits the state space of the game into an escape zone and a capture zone. This barrier and the corresponding optimal control laws are the solution to the game. The position of the barrier in the state space provides a sense of how well such a control application can perform over a sensor network.
