Stackelberg Equilibriums of Open-loop Differential Games

The paper is concerned with Stackelberg differential games for two players. Based on different assumptions on the favor of the players, several notions of Stackelberg equilibrium solution in the open-loop form are introduced, which are different from the concept given by G. Freiling et al., etc(2001). Specialization of this model to the case of linear quadratic differential game with indefinite coefficients is provided. We obtain a sufficient and necessary condition to the existence of an equilibrium by the operator method. Further, two representation formulas of the equilibrium are presented respectively via a two-point boundary value problem and a Riccati equation.