Dynamic Defender-Attacker Blotto Game

TL;DR

This paper models a dynamic graph-based resource allocation game between defenders and attackers, analyzing how graph structure and resources influence the outcome, and providing algorithms to determine victory conditions.

Contribution

It introduces a novel dynamic game framework for defender-attacker scenarios on graphs, analyzing the impact of graph topology and resources on strategic outcomes.

Findings

Outdegree of the graph affects defending difficulty.

Algorithms to identify conditions for attacker's victory.

Reachable sets used to analyze game dynamics.

Abstract

This work studies a dynamic, adversarial resource allocation problem in environments modeled as graphs. A blue team of defender robots are deployed in the environment to protect the nodes from a red team of attacker robots. We formulate the engagement as a discrete-time dynamic game, where the robots can move at most one hop in each time step. The game terminates with the attacker's win if any location has more attacker robots than defender robots at any time. The goal is to identify dynamic resource allocation strategies, as well as the conditions that determines the winner: graph structure, available resources, and initial conditions. We analyze the problem using reachable sets and show how the outdegree of the underlying graph directly influences the difficulty of the defending task. Furthermore, we provide algorithms that identify sufficiency of attacker's victory.