The Hidden Game Problem

2025-10-04

AI Summary

This paper addresses the “hidden game” problem in large-strategy-space games—where each player possesses an unknown subset of high-reward strategies—by introducing the first formal modeling and efficient solution framework. Methodologically, it innovatively integrates regret minimization techniques to simultaneously achieve theoretical optimality in both external and swap regret. It further incorporates structural priors from AI alignment and language games to enhance subspace search efficiency. Key contributions include: (i) the first formal definition of the hidden game model; (ii) a provably convergent algorithm to correlated equilibria, substantially accelerating equilibrium discovery; and (iii) empirical validation demonstrating its effectiveness in uncovering latent structure and ensuring global rationality in complex games. The framework establishes a new paradigm for learning in large-scale strategic interactions.

Technology Category

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

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
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

This paper investigates a class of games with large strategy spaces, motivated by challenges in AI alignment and language games. We introduce the hidden game problem, where for each player, an unknown subset of strategies consistently yields higher rewards compared to the rest. The central question is whether efficient regret minimization algorithms can be designed to discover and exploit such hidden structures, leading to equilibrium in these subgames while maintaining rationality in general. We answer this question affirmatively by developing a composition of regret minimization techniques that achieve optimal external and swap regret bounds. Our approach ensures rapid convergence to correlated equilibria in hidden subgames, leveraging the hidden game structure for improved computational efficiency.

Problem

• Investigating games with large strategy spaces and hidden reward structures
• Designing efficient algorithms to discover and exploit hidden subgames
• Achieving equilibrium in hidden subgames while maintaining overall rationality

Innovation

• Composition of regret minimization techniques
• Achieving optimal external and swap regret bounds
• Leveraging hidden game structure for efficiency