提出新方法求解赛车博弈中的非归一化均衡，让车辆交互更真实多样。
Non-Normalized Solutions of Generalized Nash Equilibrium in Autonomous Racing
- 基于混合互补问题（MCP）构建非归一化均衡求解框架
- 在真实赛车场景中实现多模式交互行为，突破传统方法限制
- 适合研究复杂交通博弈与自动驾驶决策的科研人员
在具有共享约束的动态博弈中，广义纳什均衡（GNE）通常采用归一化解法，假设所有玩家对共享约束使用相同的拉格朗日乘子。尽管广泛应用，该方法会排除其他潜在有价值的均衡解。本文通过三个关键贡献解决此问题：首先，用一个简单的赛车例子揭示归一化解的不足；其次，提出基于混合互补问题（MCP）的新方法，用于计算非归一化广义纳什均衡（GNE）；最后，证明所提方法克服了归一化解的局限性，在真实赛车场景中实现了更丰富的多模态交互行为。
原文摘要 · Abstract (English)
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.
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