  This paper addresses the theoretical foundations of pedestrian models for
crowd dynamics. While the topic gains momentum, widely different mathematical
approaches are actually in use, even if we only consider continuous agent-based
models. To clarify their underpinning, we first rephrase the common
hierarchical decomposition into strategic, tactical, and operational levels and
show the practical interest in preserving the continuity between the latter two
levels by working with a floor field, rather than way-points. Turning to local
navigation, we clarify how three archetypical approaches, namely, reactive
models, anticipatory models based on the idea of times to collision
(exemplified by the recently proposed ANDA model), and game theory, differ in
their extrapolation of future trajectories, and insist on the oft-overlooked
distinction between processes pertaining to decision-making and mechanical
effects in dense settings. The differences are illustrated with a comparison of
the numerical predictions of instances of these models in the simple scenario
of head-on collision avoidance between agents, by varying the walking speed and
the reaction times, notably.
