A Swarm Confrontation Method Based on Lanchester Law and Nash Equilibrium

Abstract

In this paper, more efficient allocation of forces is analyzed in the future air confrontation among unmanned aerial vehicle swarms. A novel method is proposed for swarm confrontation based on the Lanchester law and Nash equilibrium. Due to the huge number of unmanned aerial vehicles, it is not beneficial to deploy UAV forces in swarm confrontation. Moreover, unmanned aerial vehicles do not have high maneuverability in collaboration. Therefore, we propose to divide the swarms of unmanned aerial vehicles into groups, so that swarms of both sides can fight in different battlefields, which could be considered as a Colonel Blotto Game. Inspired by the double oracle algorithm, a Nash equilibrium solving method is proposed to searched for the best force allocation of the swarm confrontation. In addition, this paper proposes the concept of the boundary contact rate and carries out quantitative numerical analysis with the Lanchester law. Experiments reveal the relationship between the boundary contact rate and the optimal strategy of swarm confrontation, which could guide the force allocation in future swarm confrontation. Furthermore, the effectiveness of the division method and the double oracle-based equilibrium solving algorithm proposed in this paper is verified.