Effectively interpreting strategic interactions among multiple agents requires us to infer each agent's objective from limited information. Existing inverse game-theoretic approaches frame this challenge in terms of a "level-1" inference problem, in which we take the perspective of a third-party observer and assume that individual agents share complete knowledge of one another's objectives. However, this assumption breaks down in decentralized, real-world scenarios like urban driving and bargaining, in which agents may act based on conflicting views of one another's objectives. We demonstrate the necessity of inferring agents' different estimates of each other's objectives through empirical examples, and by theoretically characterizing the prediction error of level-1 inference on fictitious gameplay data from linear-quadratic games. To address this fundamental issue, we propose a framework for level-2 inference to address the question: "What does each agent believe about other agents' objectives?" We prove that the level-2 inference problem is non-convex even in benign settings like linear-quadratic games, and we develop an efficient gradient-based approach for identifying local solutions. Experiments on a synthetic urban driving example show that our approach uncovers nuanced misalignments that level-1 methods miss.

翻译：有效解读多智能体间的策略互动，需要我们从有限信息中推断每个智能体的目标。现有逆向博弈论方法将此挑战框定为"一级"推断问题：我们以第三方观察者视角出发，并假设个体智能体完全知晓彼此目标。然而，这一假设在去中心化的现实场景（如城市驾驶与议价博弈）中并不成立——智能体可能基于对彼此目标相互冲突的认知而采取行动。我们通过实证案例，以及在线性二次博弈虚构对局数据上理论刻画一级推断预测误差的方式，论证了推断智能体对彼此目标差异化估计的必要性。为应对这一根本问题，我们提出二级推断框架以解决核心问题："每个智能体对其他智能体目标持有何种信念？"我们证明即使在良性设置（如线性二次博弈）中，二级推断问题仍具有非凸性，并开发了一种高效的基于梯度的局部解求解方法。在合成城市驾驶场景中的实验表明，我们的方法能揭示一级方法所忽略的微妙目标错位。