An Addendum to the Problem of Zero-Sum LQ Stochastic Mean-Field Dynamic Games\\ (Extended version)

TL;DR

This paper studies a leader-follower linear quadratic mean-field game using Riccati equations to characterize equilibrium strategies and establishes conditions for solving the associated coupled Riccati equations.

Contribution

It introduces a Riccati-based approach to solve leader-follower mean-field games and provides solvability conditions for the coupled Riccati equations involved.

Findings

State-feedback strategies for Stackelberg equilibrium derived

Necessary and sufficient conditions for Riccati equations solvability established

Coupled matrix differential Riccati equations characterized

Abstract

In this paper, we first address a linear quadratic mean-field game problem with a leader-follower structure. By adopting a Riccati-type approach, we show how one can obtain a state-feedback representation of the pairs of strategies which achieve an open-loop Stackelberg equilibrium in terms of the global solutions of a system of coupled matrix differential Riccati-type equations. In the second part of this paper, we obtain necessary and sufficient conditions for the solvability of the involved coupled generalized Riccati equations.