In dynamic games with shared constraints, Generalized Nash Equilibria (GNE) are often computed using the normalized solution concept, which assumes identical Lagrange multipliers for shared constraints across all players. While widely used, this approach excludes other potentially valuable GNE. This paper addresses the limitations of normalized solutions in racing scenarios through three key contributions. First, we highlight the shortcomings of normalized solutions with a simple racing example. Second, we propose a novel method based on the Mixed Complementarity Problem (MCP) formulation to compute non-normalized Generalized Nash Equilibria (GNE). Third, we demonstrate that our proposed method overcomes the limitations of normalized GNE solutions and enables richer multi-modal interactions in realistic racing scenarios.

翻译：在具有共享约束的动态博弈中，广义纳什均衡通常使用归一化解概念进行计算，该概念假设所有参与者的共享约束具有相同的拉格朗日乘子。虽然这种方法被广泛使用，但它排除了其他潜在有价值的广义纳什均衡。本文通过三个关键贡献，探讨了归一化解在赛车场景中的局限性。首先，我们通过一个简单的赛车示例说明归一化解的不足。其次，我们提出了一种基于混合互补问题公式化的新方法，用于计算非归一化的广义纳什均衡。最后，我们证明所提出的方法克服了归一化广义纳什均衡解的局限性，并在真实的赛车场景中实现了更丰富的多模态交互。