  The local navigation of pedestrians amid a crowd is generally believed to
involve no anticipation beyond (at best) the avoidance of the most imminent
collisions. We show that current models rooted in this belief fail to reproduce
some key features experimentally evidenced when a dense static crowd is crossed
by an intruder. We identify the missing ingredient as the pedestrians' ability
to plan their motion well beyond the next interaction, whence they may accept
to move towards denser regions for a short time. To account for this effect, we
introduce a minimal model based on mean-field game theory, which proves
remarkably successful in replicating the aforementioned observations as well as
other daily-life situations involving collective behaviour in dense crowds,
such as partial metro boarding. This demonstrates the ability of game
approaches to capture the anticipatory effects at play in operational crowd
dynamics.
