This paper extends recent work in feedback-based, game-theoretic optimization. We first identify limitations of existing approaches to this problem, often requiring a priori knowledge to construct a nominal sensitivity model. Leveraging zero-order optimization techniques inspired by stochastic perturbation, we develop a model-free algorithm that allows agents to estimate these sensitivities during runtime, rather than a priori. We outline the convergence properties of this algorithm as a forward-backward operator-splitting technique. Finally, we compare this model-free algorithm’s performance to existing approaches, outlining its benefits and drawbacks.