The Learning Approach to Games

2025-02-28

AI Summary

Classical game theory models players’ strategies as scalars and relies on Nash equilibrium, neglecting internal learning architectures and cognitive constraints—thus failing to explain empirically observed non-equilibrium convergence, oscillatory behavior, and other deviations from equilibrium predictions. Method: We introduce the “learner game” paradigm, endogenously modeling players as adaptive agents implementing specific learning algorithms. Equilibrium is redefined as the stationary distribution of learning dynamics—not a static strategy profile. Our framework integrates online learning theory, stochastic approximation, mean-field analysis, and reinforcement learning dynamics. Contribution/Results: Validated across discrete games, mean-field games, and multi-agent reinforcement learning, the framework unifies explanations of non-convergence, limit cycles, and persistent oscillations. It relaxes Nash equilibrium’s implicit assumptions of full rationality and strategy homogeneity, offering a computationally tractable and interpretable foundation for modeling bounded-rational strategic interaction.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits

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: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

This work provides a unified framework for exploring games. In existing literature, strategies of players are typically assigned scalar values, and the concept of Nash equilibrium is used to identify compatible strategies. However, this approach lacks the internal structure of a player, thereby failing to accurately model observed behaviors in reality. To address this limitation, we propose to characterize players by their learning algorithms, and as their estimations intrinsically induce a distribution over strategies, we introduced the notion of equilibrium in terms of characterizing the recurrent behaviors of the learning algorithms. This approach allows for a more nuanced understanding of players, and brings the focus to the challenge of learning that players face. While our explorations in discrete games, mean-field games, and reinforcement learning demonstrate the framework's broad applicability, they also set the stage for future research aimed at specific applications.

Problem

• Unified framework for exploring games with learning algorithms.
• Addresses limitations of Nash equilibrium in modeling player behavior.
• Introduces equilibrium concept based on learning algorithm behaviors.

Innovation

• Characterizes players by learning algorithms
• Introduces equilibrium based on learning behaviors
• Applies framework to discrete and mean-field games