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

2025-08-05

AI Summary

In decentralized multi-agent strategic interactions, agents often act upon heterogeneous and inconsistent beliefs about others’ objectives; conventional level-1 inverse game-theoretic methods assume full objective common knowledge, leading to flawed reasoning. Method: We propose the first level-2 inverse game framework that explicitly models nested beliefs about agents’ objectives, integrating linear-quadratic game theory with gradient-based optimization to solve the resulting nonconvex inverse problem. Contribution: Our approach relaxes the complete-information assumption and explicitly characterizes cognitive misalignment. Evaluated on synthetic urban driving scenarios, it identifies fine-grained belief discrepancies overlooked by level-1 methods—reducing prediction error significantly—and establishes a novel paradigm for robust strategic inference in real-world interactive settings.

Technology Category

• Multiagent Systems: Adversarial Agents
• Reasoning under Uncertainty: Sequential Decision Making
• Knowledge Representation and Reasoning: Reasoning with Beliefs

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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 decision 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' heterogeneous 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 all 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.

Problem

• Infer agents' objectives from limited strategic interaction data
• Address conflicting agent views in decentralized decision scenarios
• Develop level-2 inference for agents' beliefs about objectives

Innovation

• Level-2 inference for agents' objectives estimation
• Non-convex gradient-based local solutions approach
• Uncovers nuanced misalignments in strategic interactions