This paper focuses on the performance of equalizer zero-determinant (ZD) strategies in discounted repeated Stackelberg asymmetric games. In the leader-follower adversarial scenario, the strong Stackelberg equilibrium (SSE) deriving from the opponents’ best response (BR), is technically the optimal strategy for the leader. However, computing an SSE strategy may be difficult since it needs to solve a mixed-integer program and has exponential complexity in the number of states. To this end, the authors propose an equalizer ZD strategy, which can unilaterally restrict the opponent’s expected utility. The authors first study the existence of an equalizer ZD strategy with one-to-one situations, and analyze an upper bound of its performance with the baseline SSE strategy. Then the authors turn to multi-player models, where there exists one player adopting an equalizer ZD strategy. The authors give bounds of the weighted sum of opponents’s utilities, and compare it with the SSE strategy. Finally, the authors give simulations on unmanned aerial vehicles (UAVs) and the moving target defense (MTD) to verify the effectiveness of the proposed approach.