What Do Agents Think One Another Want? Level-2 Inverse Games for Inferring Agents' Estimates of Others' Objectives

TL;DR

This paper introduces a level-2 inverse game-theoretic framework to infer what agents believe about others' objectives, addressing limitations of traditional level-1 methods in decentralized scenarios like urban driving.

Contribution

It proposes a novel level-2 inference approach, proves its non-convexity, and develops an efficient gradient-based method, demonstrating improved understanding of agents' beliefs in complex interactions.

Findings

Level-2 inference uncovers nuanced misalignments missed by level-1 methods.

The proposed approach effectively identifies agents' beliefs in synthetic urban driving scenarios.

Level-2 inference is non-convex even in simple linear-quadratic games.

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.