A Unified Relation Analysis of Linear-quadratic Mean-field Game, Team and Control

TL;DR

This paper provides a comprehensive analysis of linear-quadratic mean-field game, team, and control problems, exploring their interrelations and offering insights applicable to large-population decision systems.

Contribution

It systematically analyzes the relationships among mean-field game, team, and control problems within a unified stochastic linear-quadratic framework, including indefinite weights and controlled diffusion.

Findings

Interrelations among MG, MT, and MC are systematically characterized.

Structural insights into large-population decision problems are provided.

The analysis applies to general stochastic linear-quadratic settings.

Abstract

This paper revisits well-studied dynamic decisions of weakly coupled large-population (LP) systems. Specifically, three types of LP decision problems: mean-field game (MG), mean-field team (MT), and mean-field-type control (MC), are completely analyzed in a general stochastic linear-quadratic setting with controlled-diffusion in state dynamics and indefinite weight in cost functional. More importantly, interrelations among MG, MT and MC are systematically discussed; some relevant interesting findings are reported that may be applied to a structural analysis of general LP decisions.