Optimizing the Locations of Opposing Teams Using Adversarial Voronoi Regions

In this paper we introduce the Adversarial Voronoi Regions (AVR) as a way of evaluating and updating the states of opposing teams. While many multi-agent problems focus on cooperative tasks like search and rescue, task allocation, or distributed sensing, there are also adversarial settings where teams compete to maximize their own outcomes, often at the expense of the opposing team. Such scenarios include zero-sum games, various team sports, pursuit-evasion problems, and business competition.We show how the AVR concept can be used to formulate an optimization problem that captures the utility of the positions of agents in adversarial scenarios, such as competing business locations, team sport tactics, and security agents handling potential threats. We also derive the analytical gradient of the AVR utility and show how this can be used to dynamically control the team over time, or to find locally optimal configurations. Then we show that for an agent with a single adversarial neighbor, the gradient drives the agent closer to its neighbor and toward the center of mass of the edge separating them. Finally, we illustrate the approach with practical examples, demonstrating its adaptability in dynamic and competitive scenarios.