Min-max saddle point games appear in a wide range of applications in machine\nleaning and signal processing. Despite their wide applicability, theoretical\nstudies are mostly limited to the special convex-concave structure. While some\nrecent works generalized these results to special smooth non-convex cases, our\nunderstanding of non-smooth scenarios is still limited. In this work, we study\nspecial form of non-smooth min-max games when the objective function is\n(strongly) convex with respect to one of the player's decision variable. We\nshow that a simple multi-step proximal gradient descent-ascent algorithm\nconverges to $\\epsilon$-first-order Nash equilibrium of the min-max game with\nthe number of gradient evaluations being polynomial in $1/\\epsilon$. We will\nalso show that our notion of stationarity is stronger than existing ones in the\nliterature. Finally, we evaluate the performance of the proposed algorithm\nthrough adversarial attack on a LASSO estimator.\n