Learning generalized Nash equilibria from pairwise preferences

2026-03-17

AI Summary

This work proposes a generalized Nash equilibrium problem (GNEP) solution method that relies solely on pairwise preference feedback from agents, without requiring access to explicit utility functions or best-response information. By integrating preference learning with an active learning strategy, the approach effectively balances exploration and exploitation to select maximally informative query samples, thereby constructing a learnable GNEP model that approximates the true equilibrium. As the first framework capable of learning GNEP solutions without explicit utility representations or optimal-response feedback, it successfully recovers ground-truth equilibria in both linear-quadratic regulator games and standard GNEP benchmark problems, demonstrating its feasibility and accuracy.

Technology Category

• Multiagent Systems: Mechanism Design
• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Equilibrium

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Generalized Nash Equilibrium Problems (GNEPs) arise in many applications, including non-cooperative multi-agent control problems. Although many methods exist for finding generalized Nash equilibria, most of them rely on assuming knowledge of the objective functions or being able to query the best responses of the agents. We present a method for learning solutions of GNEPs only based on querying agents for their preference between two alternative decisions. We use the collected preference data to learn a GNEP whose equilibrium approximates a GNE of the underlying (unknown) problem. Preference queries are selected using an active-learning strategy that balances exploration of the decision space and exploitation of the learned GNEP. We present numerical results on game-theoretic linear quadratic regulation problems, as well as on other literature GNEP examples, showing the effectiveness of the proposed method.

Problem

• Generalized Nash Equilibrium
• preference learning
• active learning
• multi-agent systems
• equilibrium learning

Innovation

• Generalized Nash Equilibrium
• Preference-based Learning
• Active Learning
• Multi-agent Systems
• Game Theory