Deriving strategies for multiple agents under adversarial scenarios poses a significant challenge in attaining both optimality and efficiency. In this paper, we propose an efficient defense strategy for cooperative defense against a group of attackers in a convex environment. The defenders aim to minimize the total number of attackers that successfully enter the target set without prior knowledge of the attacker's strategy. Our approach involves a two-scale method that decomposes the problem into coordination against a single attacker and assigning defenders to attackers. We first develop a coordination strategy for multiple defenders against a single attacker, implementing online convex programming. This results in the maximum defense-winning region of initial joint states from which the defender can successfully defend against a single attacker. We then propose an allocation algorithm that significantly reduces computational effort required to solve the induced integer linear programming problem. The allocation guarantees defense performance enhancement as the game progresses. We perform various simulations to verify the efficiency of our algorithm compared to the state-of-the-art approaches, including the one using the Gazabo platform with Robot Operating System.

翻译：在对抗性多智能体场景中推导策略在实现最优性和效率方面均面临重大挑战。本文针对凸环境中的协同防御问题，提出了一种针对攻击者群体的高效防御策略。防御方旨在未知攻击者先验策略的情况下，最小化成功突入目标集合的攻击者总数。我们的方法采用两尺度分解策略：首先将问题分解为针对单一攻击者的协同防御，再执行防御者-攻击者分配。首先，我们为多防御者对抗单一攻击者开发协同策略，采用在线凸规划方法。该策略定义了防御者成功拦截单一攻击者的最大防御获胜初始联合状态区域。随后，我们提出一种分配算法，显著降低了求解衍生整数线性规划问题的计算开销。该分配机制能保证随着博弈进程推进，防御性能持续提升。通过多组仿真实验（包括基于机器人操作系统的Gazebo平台验证），我们验证了该算法相较于现有先进方法的效率优势。