Numerical method for finding a static Stackelberg-Nash equilibrium: The case of favorable followers

In this paper a regularized version of the "gradient projection technique" is suggested to be applied for finding Stackelberg-Nash equilibrium in a multi-participant game. A N-person game is examined in this work. There exist two levels of hierarchy in decision making: the first one consists of a leader and the second one is formed by (N - 1) followers. The followers react to the leader\´s announced strategy by playing according to the Nash equilibrium concept among themselves selecting those of equilibriums which is most favorable for the leader. Here, applying the gradient projection technique, the Stackelberg-Nash equilibrium is attained. The convergence of the suggested procedure to one of Stackelberg-Nash equilibrium is analyzed. Simulation results illustrate the feasibility and the performance of this method.