Bounded Rationality Equilibrium Learning in Mean Field Games

TL;DR

This paper introduces bounded rationality concepts into mean field games using quantal response equilibria and receding horizon models, along with algorithms for learning these equilibria, to better reflect realistic agent behavior.

Contribution

It develops novel bounded rationality models for MFGs, combining QRE and receding horizon approaches, and proposes algorithms for their equilibrium learning.

Findings

QRE and RH MFGs effectively model bounded rationality.

Algorithms successfully learn these equilibria in various examples.

Bounded rationality models differ from traditional Nash equilibria in practical scenarios.

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.