This paper discusses formulations and algorithms which allow a number of agents to collectively solve problems involving both (non-convex) minimization and (concave) maximization operations. These problems have a number of interesting applications in information processing and machine learning, and in particular can be used to model an adversary learning problem called network data poisoning. We develop a number of algorithms to efficiently solve these non-convex min-max optimization problems, by combining techniques such as gradient tracking in the decentralized optimization literature and gradient descent-ascent schemes in the min-max optimization literature. Also, we establish convergence to a first order stationary point under certain conditions. Finally, we perform experiments to demonstrate that the proposed algorithms are effective in the data poisoning attack.