Approximate solutions to a class of nonlinear Stackelberg differential games

A two-player nonlinear Stackelberg differential game with player 1 and player 2 as leader and follower, respectively, is considered. The feedback Stackelberg solutions to such games rely on the solution of two coupled partial differential equations (PDEs) for which closed-form solutions cannot in general be found. A method for constructing strategies satisfying partial differential inequalities in place of the PDEs is presented. It is shown that these constitute approximate solutions to the differential game. The theory is illustrated by a numerical example.