Dynamic Adversarial Resource Allocation: the dDAB Game

Abstract

This work introduces the dynamic Defender-Attacker Blotto (dDAB) game, extending the classical static Blotto game to a dynamic resource allocation setting over graphs. In the dDAB game, a defender is required to maintain numerical superiority against attacker resources across a set of key nodes in a connected graph. The engagement unfolds as a discrete-time game, where each player reallocates its resources in turn, with resources allowed to move at most one hop per time step. The primary goal is to determine the necessary and sufficient amount of defender resources required to guarantee sustained defense, along with the corresponding strategies. To address the central challenge arising from graph-constrained resource reallocation, we conduct a reachability analysis, starting with simplified settings where attacker resources act as a single cohesive group. We then extend the framework to allow attacker resources to split and merge arbitrarily, and construct defender strategies using superposition principles. A set-based dynamic programming algorithm is developed to compute the optimal strategies, as well as the minimum amount of defender resources to ensure successful defense. The effectiveness of our approach is demonstrated through numerical simulations and hardware experiments on the Georgia Tech Robotarium platform.