Travellers route choice dynamics with endogenous reliability of ATIS are modelled.Joint strategy fictitious play model best describes route choice learning process.In case of low accuracy of information, choice behaviour tends towards randomness. This paper aims to model the traveller's day-to-day route choice in the case of an Advanced Traveller Information System (ATIS) through two learning paradigms: reinforcement-based and belief-based. The reinforcement learning approach is adopted in both a basic version and an extended one. Similarly, the belief-learning approach is adopted in both a Joint Strategy Fictitious Play version and in a Bayesian-learning one. All the models are compared and validated based on data collected by means of a stated preference experiment. The models explicitly account for the reliability of the information system, as this interacts with the inherent dispersion of network travel times and determines the overall level of uncertainty affecting the travellers adaptive learning behaviour. The experiment is then designed to simulate different levels of reliability for the ATIS. Results show that for intermediate and high levels of information accuracy, joint strategy fictitious play best predicts the respondents route choice behaviour under information provision, suggesting that a best-reply strategy is used by travellers for their route choices. In low information accuracy, the result suggests the payoff variability moves the choice behaviour toward randomness. The proposed approach provides useful tools to model travellers adaptive route choice behaviour and contributes to the support of effective ATIS design.