Path Defense in Dynamic Defender-Attacker Blotto Games (dDAB) with Limited Information

We consider a path guarding problem in dynamic Defender-Attacker Blotto games (dDAB), where a team of robots must defend a path in a graph against adversarial agents. Multi-robot systems are particularly well suited to this application, as recent work has shown the effectiveness of these systems in related areas such as perimeter defense and surveillance. When designing a defender policy that guarantees the defense of a path, information about the adversary and the environment can be helpful and may reduce the number of resources required by the defender to achieve a sufficient level of security. In this work, we characterize the necessary and sufficient number of assets needed to guarantee the defense of a shortest path between two nodes in dDAB games when the defender can only detect assets within $k$-hops of a shortest path. By characterizing the relationship between sensing horizon and required resources, we show that increasing the sensing capability of the defender greatly reduces the number of defender assets needed to defend the path.