Feedback strategies for discrete-time linear-quadratic two-player descriptor games

Marc Jungers (1)

1 CRAN - Centre de Recherche en Automatique de Nancy

This paper deals with discrete-time linear-quadratic descriptor two-player games. The two frameworks of Nash and Stackelberg strategies with feedback information structure are considered. The aim is to provide sufficient conditions ensuring, for any initial state, the existence and the uniqueness of a tri-trajectory, gathering the state and the controls of the two players, which reaches the equilibrium. The provided results are mainly based on a discrete-time matrix block formulation. The provided algorithms consist in an iterative backward in time procedure, issued from Dynamic Programming. Numerical examples illustrate this approach and the particular case of explicit systems is recovered for both kinds of strategies.

Mots clés: Descriptor games; Game theory; Feedback information structure; Nash strategy; Stackelberg strategy; Matrix block formulation

Domaines: Automatique / Robotique

Marc Jungers. Feedback strategies for discrete-time linear-quadratic two-player descriptor games. Linear Algebra and its Applications, 2014, 440, pp.1-23. ⟨10.1016/j.laa.2013.10.050⟩. ⟨hal-00881365⟩