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 presents a novel method based on the Mixed Complementarity Problem (MCP) formulation to compute non-normalized GNE, expanding the solution space. We also propose a systematic approach for selecting the optimal GNE based on predefined criteria, enhancing practical flexibility. Numerical examples illustrate the methods effectiveness, offering an alternative to traditional normalized solutions.

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对共享约束具有相同的拉格朗日乘子。尽管这种方法被广泛使用，但它排除了其他可能具有价值的广义纳什均衡。本文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，从而扩展了解空间。我们还提出了一种基于预定义准则选择最优广义纳什均衡的系统性方法，增强了实际应用的灵活性。数值算例证明了该方法的有效性，为传统的归一化解提供了替代方案。