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Regularized versions of the rdquoProjectional Gradient Techniquerdquo and the ldquoExtraproximal Methodrdquo are suggested to be applied for finding Stackelberg-Nash equilibrium in a multi-participant static game. A comparative between these methods is shown. 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 (N - 1)-followers. The followers react to the leaderpsilas announced strategy by playing according to the Nash equilibrium concept among themselves selecting those of equilibriums which is most favorable or unfavorable for the leader. The convergence of the suggested procedure is analyzed. Simulation results illustrate the feasibility of this method.