The utilization of artificial intelligence (AI) in the engagement has been a key research topic in the defense field during the last decade. To pursue this utilization, it is imperative to acquire a realistic simulation to train an AI engagement agent with a synthetic, but realistic field. This paper is a case study of training an AI agent to operate with a hardware realism in the air-warfare dog-fighting. Particularly, this paper models the pursuit of an opponent in the dog-fighting setting with a gun-only engagement. In this context, the AI agent requires to make a decision on the pursuit style and intensity. We developed a realistic hardware simulator and trained the agent with a reinforcement learning. Our training shows a success resulting in a lead pursuit with a decreased engagement time and a high reward.