Unicity of the solution is an important character of the Dynamic Traffic Assignment (DTA) problem. Beckman et al. (1956) indicate the importance of unicity and stability of the solution. The conditions of unicity have been properly reviewed by Iryo (2013) for flow-based DTA by considering the different approach to solving the DTA problem. Moreover, many researches have been done to prove the unicity of DTA solutions on flow-based dynamic traffic model with several assumptions and limitations on traffic network model (Mounce, 2007; Mounce and Smith, 2007; Iryo 2011; Iryo 2015; Iryo and Smith, 2017). This study adapts the conditions to trip-based DTA wherein each traveler is defined as an individual. A key characteristic for unicity is strictly monotone path travel time function with respect to the number of travelers that use the path. There is no guaranty to hold the monotonicity condition in the multimodal urban transportation network (Mounce, 2001). This study aims to investigate the end result of the evolution of a transportation system over a long-term day to day learning process. Mathematically speaking, we are going to address the impact of initial solutions in the day-to-day multimodal DTA.