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

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 g...

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Bibliographic Details
Published in:Automatica (Oxford) 2023-07, Vol.153, p.111007, Article 111007
Main Authors: Aberkane, Samir, Dragan, Vasile
Format: Article
Language:English
Subjects:
Engineering Sciences
Mathematics
Mean field
Sackelberg equilibrium
Stochastic Riccati equations
Zero-sum stochastic dynamic games
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Summary: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.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2023.111007