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

Samir Aberkane; Vasile Dragan

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arXiv · 2302.09609

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

Samir Aberkane·Vasile Dragan

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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.

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BibTeX RIS

Samir Aberkane, Vasile Dragan. 2023-02-19. An Addendum to the Problem of Zero-Sum LQ Stochastic Mean-Field Dynamic Games\\ (Extended version). https://arxiv.org/abs/2302.09609

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