Cooperative or Competitive? Understanding the Interaction between Attention Heads From A Game Theory Perspective

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.