The multi-modal railway network, comprising high-speed rail (HSR), intercity rail (ICR), suburban rail (SUR), and urban rail transit (URT), has been gaining increasing attention due to its reliability and social benefits. These different rail transit modes often cooperate to provide seamless multi-modal travel services for long-distance passengers, while simultaneously facing competition due to overlapping passenger demand. However, most existing studies on ticket pricing and train scheduling do not fully account for the competition–cooperation relationships among these four rail transit modes. To address this gap, this study presents a multi-leader–follower game model that integrates ticket pricing and train scheduling (including line planning and timetabling) while considering the competitive and cooperative interactions within the multi-modal railway network. The model incorporates a simulation-based passenger assignment approach at the lower level and a decision-making framework at the upper level, aiming to approximate a Nash equilibrium solution among the various railway operators. The bus system is introduced only to provide a realistic competitive background, preventing a purely railway-monopolized setting and allowing us to better analyze the cooperative–competitive strategies among the four railway systems. An improved Nash Q-learning algorithm is developed to iteratively determine the approximated Nash equilibrium solution for the proposed multi-leader–follower game model. The effectiveness of the proposed method is demonstrated in a case study based on the multi-modal railway network in Jiangsu Province and Shanghai, China. Our results show that the proposed method can effectively optimize both ticket pricing and train scheduling in the multi-modal railway network under various competition–cooperation scenarios. A viable cooperation strategy involves encouraging passengers with short-distance trips to use urban transport modes (such as SUR and URT) while reserving more available seats on intercity transport modes (like HSR and ICR) for long-distance passengers. This strategy helps optimize the overall efficiency of the multi-modal transportation system.