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<p>In dynamic confrontation scenarios such as UAV swarm confrontations, enabling a small number of superior defenders to efficiently coordinate and intercept a larger number of weaker attackers is the key challenge to achieving “defeating quantity with quality.” This “Target-Attacker-Defender” game problem, due to its high-dimensional state space and the multi-stage dependency of offensive and defensive strategies, makes traditional differential game methods difficult to solve directly. To address the dynamic adversarial scenario where a minority of strong defenders collaboratively intercepts numerous weak attackers, this paper proposes a collaborative control strategy based on the auction algorithm and Stackelberg game theory, aiming to solve the coupling optimization problem of multi-defender target allocation, collaborative decision-making, and attacker intelligent evasion. The research focuses on constructing a multi-stage sequential game model. By integrating an improved auction algorithm-based dynamic target allocation mechanism, a hierarchical sampling strategy, and a model predictive control (MPC) solving framework, efficient interception of attackers by defenders is achieved, validating the theoretical feasibility of “winning by quality over quantity.” The study shows that the proposed multi-defender collaborative interception strategy realizes the coupling optimization of target allocation, dynamic decision-making, and attacker evasion, demonstrating high interception efficiency and robustness in simulation scenarios. Simulation experiments verified the effectiveness of the strategy in a typical “3 defenders versus 12 attackers” scenario. The results show that the strategy achieved a 100% interception success rate, with balanced task allocation among the defenders. A parameter sensitivity analysis (based on 500 Latin hypercube samples) further quantified the impact of key parameters, revealing that the prediction horizon (contributing 56.81% to the improvement in interception rate) and the defenders’ maximum acceleration (contributing 31.94%) are the dominant factors determining system performance.</p>

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Winning against the odds: A study on cooperative interception of weak attackers by strong defenders based on Stackelberg game

  • 期刊论文

  • 发表日期：

    2026年4月27日

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  • Jian’an Zong,
  • Xianzhong Gao,
  • Jialong Zhang,
  • Haibin Duan,
  • Yue Zhang,
  • Lei Bao,
  • Zhongxi Hou

摘要

In dynamic confrontation scenarios such as UAV swarm confrontations, enabling a small number of superior defenders to efficiently coordinate and intercept a larger number of weaker attackers is the key challenge to achieving “defeating quantity with quality.” This “Target-Attacker-Defender” game problem, due to its high-dimensional state space and the multi-stage dependency of offensive and defensive strategies, makes traditional differential game methods difficult to solve directly. To address the dynamic adversarial scenario where a minority of strong defenders collaboratively intercepts numerous weak attackers, this paper proposes a collaborative control strategy based on the auction algorithm and Stackelberg game theory, aiming to solve the coupling optimization problem of multi-defender target allocation, collaborative decision-making, and attacker intelligent evasion. The research focuses on constructing a multi-stage sequential game model. By integrating an improved auction algorithm-based dynamic target allocation mechanism, a hierarchical sampling strategy, and a model predictive control (MPC) solving framework, efficient interception of attackers by defenders is achieved, validating the theoretical feasibility of “winning by quality over quantity.” The study shows that the proposed multi-defender collaborative interception strategy realizes the coupling optimization of target allocation, dynamic decision-making, and attacker evasion, demonstrating high interception efficiency and robustness in simulation scenarios. Simulation experiments verified the effectiveness of the strategy in a typical “3 defenders versus 12 attackers” scenario. The results show that the strategy achieved a 100% interception success rate, with balanced task allocation among the defenders. A parameter sensitivity analysis (based on 500 Latin hypercube samples) further quantified the impact of key parameters, revealing that the prediction horizon (contributing 56.81% to the improvement in interception rate) and the defenders’ maximum acceleration (contributing 31.94%) are the dominant factors determining system performance.