An addendum to the problem of zero-sum LQ stochastic mean-field dynamic games

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.