Analytical solution for an open-loop Stackelberg game

A method to solve the two point boundary value problem (TPBVP) occurring in open-loop Stackelberg strategy for linear-quadratic games is presented. By writing in a special order the necessary conditions that an open-loop Stackelberg solution must satisfy, a Hamiltonian matrix comes out and its properties are exploited to solve the TPBVP. The solution procedure becomes similar to the one used to solve a matrix Riccati equation by the eigenvector method. A simple example is given to illustrate the proposed method.