Secure signal authentication is arguably one of the most challenging problems in the Internet of Things (IoT) environment, due to the large-scale nature of the system and its susceptibility to man-in-the-middle and eavesdropping attacks. In this paper, a novel deep learning method is proposed for dynamic authentication of IoT signals to detect cyber attacks. The proposed learning framework, based on a long short-term memory (LSTM) structure, enables the IoT devices (IoTDs) to extract a set of stochastic features from their generated signal and dynamically watermark these features into the signal. This method enables the cloud, which collects signals from the IoT devices, to effectively authenticate the reliability of the signals. Moreover, in massive IoT scenarios, since the cloud cannot authenticate all the IoTDs simultaneously due to computational limitations, a game-theoretic framework is proposed to improve the cloud's decision making process by predicting vulnerable IoTDs. The mixed-strategy Nash equilibrium (MSNE) for this game is derived and the uniqueness of the expected utility at the equilibrium is proven. In the massive IoT system, due to a large set of available actions for the cloud, it is shown that analytically deriving the MSNE is challenging and, thus, a learning algorithm proposed that converges to the MSNE. Moreover, in order to cope with the incomplete information case in which the cloud cannot access the state of the unauthenticated IoTDs, a deep reinforcement learning algorithm is proposed to dynamically predict the state of unauthenticated IoTDs and allow the cloud to decide on which IoTDs to authenticate. Simulation results show that, with an attack detection delay of under 1 second the messages can be transmitted from IoT devices with an almost 100% reliability.