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We present a conceptual framework for the dynamic traffic resources allocation problem in a situation of elastic demand among customers. We introduce an activity-based model to express customers' successive actions and transfers in order to capture the essential aspect of transfers as a derived demand. We focus on the decision-making of customers, in that they only use a mobility service when their space-time prism constraints represent the worst case. Under the setting with such elastic demand, we characterize a class of dynamic traffic resources allocation mechanisms that strictly keep space-time prism constraints of users and capacity constraints of traffic resources. Within the class of mechanisms, we show the optimal mechanism that maximizes discounted social welfare and show an exact solution algorithm for both, myopic and non-myopic settings, using the zero-suppressed binary decision diagram. We also present approximation algorithms that are still included in the class of mechanisms. In numerical studies, we showed that our proposed algorithm works effectively in settings with high rejection rates, meaning that this algorithm can be used to focus on the behavior of latent customers who have not used mobility services so far. The proposed non-myopic algorithm is suitable to design services for limited small number of customers, for example a car-sharing services for prescribed members, while the proposed myopic algorithm is suitable for designing services for a large unspecified number of customers, for example, a ride-sharing service in a large city.