A Unified Relation Analysis of Linear-Quadratic Mean-Field Game, Team, and Control

This article revisits well-studied dynamic decisions in 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 and interesting findings are reported that may be applied to a structural analysis of general LP decisions.