Strategy Representation Analysis for Patrolling Games

This paper considers the problem of patrolling multiple targets in a Euclidean environment by a single patrolling unit. We use game-theoretic approach and model the problem as a two-player zero-sum game in the extensive form. Based on the existing work in the domain of patrolling we propose a novel mathematical non-linear program for finding strategies in a discretized problem, in which we introduce a general concept of internal states of the patroller. We experimentally evaluate game value for the patroller for various graphs and strategy representations. The results suggest that adding internal states for the patroller yields better results in comparison to adding choice nodes in the used discretization.