Multi-robot coordination often exhibits hierarchical structure, with some robots' decisions depending on the planned behaviors of others. While game theory provides a principled framework for such interactions, existing solvers struggle to handle mixed information structures that combine simultaneous (Nash) and hierarchical (Stackelberg) decision-making. We study N-robot forest-structured mixed-hierarchy games, in which each robot acts as a Stackelberg leader over its subtree while robots in different branches interact via Nash equilibria. We derive the Karush-Kuhn-Tucker (KKT) first-order optimality conditions for this class of games and show that they involve increasingly high-order derivatives of robots' best-response policies as the hierarchy depth grows, rendering a direct solution intractable. To overcome this challenge, we introduce a quasi-policy approximation that removes higher-order policy derivatives and develop an inexact Newton method for efficiently solving the resulting approximated KKT systems. We prove local exponential convergence of the proposed algorithm for games with non-quadratic objectives and nonlinear constraints. The approach is implemented in a highly optimized Julia library (MixedHierarchyGames.jl) and evaluated in hardware and simulated multi-agent experiments, demonstrating real-time convergence for complex mixed-hierarchy information structures.

翻译：多机器人协调通常表现出层次结构，某些机器人的决策依赖于其他机器人的计划行为。尽管博弈论为此类交互提供了原则性框架，但现有求解器难以处理融合同步（纳什）与层次（斯塔克尔伯格）决策的混合信息结构。我们研究N机器人森林结构混合层次博弈，其中每个机器人作为其子树的斯塔克尔伯格领导者，而不同分支间的机器人通过纳什均衡交互。我们推导出此类博弈的Karush-Kuhn-Tucker (KKT)一阶最优性条件，并证明随着层次深度增加，这些条件涉及机器人最佳响应策略的越来越高阶导数，使得直接求解不可行。为克服此挑战，我们引入消除高阶策略导数的准策略近似，并开发非精确牛顿法以高效求解近似后的KKT系统。我们证明该算法在非二次目标与非线性约束博弈中具有局部指数收敛性。该方法在高度优化的Julia库（MixedHierarchyGames.jl）中实现，并通过硬件实验与仿真多智能体评估，展示了复杂混合层次信息结构的实时收敛能力。