Adversarial attacks have consistently posed a critical challenge to the reliability of deep learning models. This warrants heightened concern towards malicious cyber attacks in sensitive application domains of cybersecurity where such learning models are relied upon to detect and mitigate adversarial threats. In this work, we present a method to improve the robustness of network intrusion detection system (NIDS) models by leveraging a game theoretical adversarial training algorithm with a variational adversary to generate optimal perturbations causing misclassifications. Subsequently, we show that integrating such adversarially manipulated data samples into the training algorithm leads to an improvement in the resilience of the NIDS classifiers against such attacks. To validate our method, we also simulate cyber attacks in a Software Defined Networking (SDN) environment, generating synthetic traffic data for adversarial training. We detail the setup for this simulation, providing a reproducible framework for adversarial training in security contexts. This complements our experiments on widely used benchmark datasets for network intrusion detection systems such as CSE-CIC-IDS2018 and NSL-KDD. We also assess the generality of the proposed method by applying it to the emerging Kolmogorov Arnold Networks (KANs). Our results confirm that the game theory based adversarial training algorithm significantly enhances the robustness of KANs, highlighting the value of our approach.