Short-video applications have attracted substantial user traffic. However, these platforms also foster problematic usage patterns, commonly referred to as short-video addiction, which pose risks to both user health and the sustainable development of platforms. Prior studies on this issue have primarily relied on questionnaires or volunteer-based data collection, which are often limited by small sample sizes and population biases. In contrast, short-video platforms have large-scale behavioral data, offering a valuable foundation for analyzing addictive behaviors. To examine addiction-aware behavior patterns, we combine economic addiction theory with users' implicit behavior captured by recommendation systems. Our analysis shows that short-video addiction follows functional patterns similar to traditional forms of addictive behavior (e.g., substance abuse) and that its intensity is consistent with findings from previous social science studies. To develop a simulator that can learn and model these patterns, we introduce a novel training framework, AddictSim. To consider the personalized addiction patterns, AddictSim uses a mean-to-adapted strategy with group relative policy optimization training. Experiments on two large-scale datasets show that AddictSim consistently outperforms existing training strategies. Our simulation results show that integrating diversity-aware algorithms can mitigate addictive behaviors well.