@inproceedings{qu-etal-2025-cooperative,
    title = "Cooperative or Competitive? Understanding the Interaction between Attention Heads From A Game Theory Perspective",
    author = "Qu, Xiaoye  and
      Yu, Zengqi  and
      Liu, Dongrui  and
      Wei, Wei  and
      Liu, Daizong  and
      Dong, Jianfeng  and
      Cheng, Yu",
    editor = "Che, Wanxiang  and
      Nabende, Joyce  and
      Shutova, Ekaterina  and
      Pilehvar, Mohammad Taher",
    booktitle = "Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)",
    month = jul,
    year = "2025",
    address = "Vienna, Austria",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingestion-acl-25/2025.acl-long.688/",
    pages = "14079--14099",
    ISBN = "979-8-89176-251-0",
    abstract = "Despite the remarkable success of attention-based large language models (LLMs), the precise interaction mechanisms between attention heads remain poorly understood. In contrast to prevalent methods that focus on individual head contributions, we rigorously analyze the intricate interplay among attention heads through a novel framework based on the Harsanyi dividend, a concept from cooperative game theory. Our analysis reveals that significant positive Harsanyi dividends are sparsely distributed across head combinations, indicating that most heads do not contribute cooperatively. Moreover, certain head combinations exhibit negative dividends, indicating implicit competitive relationships. To further optimize the interactions among attention heads, we propose a training-free Game-theoretic Attention Calibration (GAC) method. Specifically, GAC selectively retains heads demonstrating significant cooperative gains and applies fine-grained distributional adjustments to the remaining heads. Comprehensive experiments across 17 benchmarks demonstrate the effectiveness of our proposed GAC and its superior generalization capabilities across diverse model families, scales, and modalities. Crucially, the discovered interaction phenomena offer a path toward a deeper understanding of the behaviors of LLMs."
}