What Do Agents Think One Another Want? Level-2 Inverse Games for Inferring Agents' Estimates of Others' Objectives
Hamzah I. Khan, Jingqi Li, David Fridovich-Keil
TL;DR
The paper tackles the challenge of interpreting multi-agent strategic interactions when agents hold heterogeneous beliefs about others' objectives, arguing that standard level-1 inverse game methods are insufficient. It develops a level-2 inverse game framework where each agent optimizes its own objective while forming estimates of others' objectives, and a third party infers both the objectives and the beliefs by solving a series of coupled Nash problems. The authors prove non-convexity in level-2 inference for linear-quadratic games and derive loss bounds illustrating level-1 inadequacy under belief misalignment, then propose a differentiable MCP-based gradient solver that scales to offline and online settings. Empirical results on a lane-change driving scenario show level-2 inference uncovers critical misalignments and deadlock conditions that level-1 cannot explain, suggesting practical benefits for safer autonomous planning and regulator-informed traffic optimization. The work lays groundwork for extending level-2 reasoning to more complex nonlinear, stochastic environments and for formal analysis of observability of level-2 parameters.
Abstract
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.