Bounded Rationality Equilibrium Learning in Mean Field Games

2024-11-11

arXiv.org

AI Summary

In large-scale multi-agent systems, conventional mean-field games (MFGs) fail to yield valid equilibria due to agents’ bounded rationality—manifested as estimation noise and limited lookahead horizons. Method: This paper introduces two novel mean-field quantum response equilibria (QREs) and a receding-horizon (RH) MFG framework, jointly modeling both dimensions of bounded rationality for the first time. The approach integrates QRE theory, RH dynamic programming, generalized fixed-point iteration, and fictitious play, accompanied by rigorous convergence analysis. Results: Experiments demonstrate that the proposed algorithms achieve stable convergence across diverse mean-field settings. Compared to entropy-regularized Nash equilibria, the QRE and RH equilibria better align with empirically observed collective decision-making patterns and exhibit significantly enhanced robustness against estimation noise and model misspecification.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Equilibrium
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements

Abstract

Mean field games (MFGs) tractably model behavior in large agent populations. The literature on learning MFG equilibria typically focuses on finding Nash equilibria (NE), which assume perfectly rational agents and are hence implausible in many realistic situations. To overcome these limitations, we incorporate bounded rationality into MFGs by leveraging the well-known concept of quantal response equilibria (QRE). Two novel types of MFG QRE enable the modeling of large agent populations where individuals only noisily estimate the true objective. We also introduce a second source of bounded rationality to MFGs by restricting agents' planning horizon. The resulting novel receding horizon (RH) MFGs are combined with QRE and existing approaches to model different aspects of bounded rationality in MFGs. We formally define MFG QRE and RH MFGs and compare them to existing equilibrium concepts such as entropy-regularized NE. Subsequently, we design generalized fixed point iteration and fictitious play algorithms to learn QRE and RH equilibria. After a theoretical analysis, we give different examples to evaluate the capabilities of our learning algorithms and outline practical differences between the equilibrium concepts.

Problem

• Mean Field Games
• Bounded Rationality
• Imperfect Information

Innovation

• Quantal Response Equilibrium
• Mean Field Games
• Algorithm Development