Weak Stackelberg strategy with closed-loop information structure

Marc Jungers (1) , Emmanuel Trélat (2) , Hisham Abou-Kandil (3)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
3 SATIE - Systèmes et Applications des Technologies de l'Information et de l'Energie

This paper deals with the weak Stackelberg strategy in the case of a closed-loop information structure. Two–player differential games are considered with one leader and one follower. We first derive necessary conditions for the Stackelberg equilibrium in the general case of nonlinear criteria for finite time horizon games which lead to an expression of the optimal controls along the associated tra jectory. Then, using focal point theory, the necessary conditions are also shown to be sufficient and lead to cheap control. The set of initial states allowing the existence of an optimal trajectory is emphasized. The Linear Quadratic case is detailed to illustrate these results.

Mots clés: Stackelberg strategy; Game theory; Multi-criteria optimization; Closed-loop information structure; Bilevel optimization problem

Domaines: Optimisation et contrôle [math.OC]

Marc Jungers, Emmanuel Trélat, Hisham Abou-Kandil. Weak Stackelberg strategy with closed-loop information structure. 2010. ⟨hal-00086780v2⟩