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As Large Language Models (LLMs) transition into autonomous multi-agent ecosystems, robust minimax training becomes essential yet remains prone to instability when highly non-linear policies induce extreme local curvature in the inner maximization. Standard remedies that enforce global Jacobian bounds are overly conservative, suppressing sensitivity in all directions and inducing a large Price of Robustness. We introduce Adversarially-Aligned Jacobian Regularization (AAJR), a trajectory-aligned approach that controls sensitivity strictly along adversarial ascent directions. We prove that AAJR yields a strictly larger admissible policy class than global constraints under mild conditions, implying a weakly smaller approximation gap and reduced nominal performance degradation. Furthermore, we derive step-size conditions under which AAJR controls effective smoothness along optimization trajectories and ensures inner-loop stability. These results provide a structural theory for agentic robustness that decouples minimax stability from global expressivity restrictions.