Extraproximal Method Application for a Stackelberg–Nash Equilibrium Calculation in Static Hierarchical Games

A regularized version of the extraproximal method is suggested for finding the Stackelberg-Nash equilibrium in a multiparticipant static game. There exist two levels of hierarchy in decision making: The first one consists of a leader decision, and the second one is formed by the decisions of the (N - 1) followers. The followers react to the leader´s announced strategy by playing according to the Nash equilibrium concept, selecting among themselves that whose equilibrium is most favorable or unfavorable for the leader. Here, applying the extraproximal technique, the Stackelberg-Nash equilibrium is attained. The convergence of the suggested procedure is analyzed. Simulation results illustrate the feasibility of this method.