The short-term ('operational') dynamics of pedestrian crowds are generally thought to involve no anticipation, except perhaps the avoidance of the most imminent collisions. We show that current models rooted in this belief fail to reproduce essential features experimentally observed when a static crowd is crossed by an intruder. We identify the missing ingredient as the pedestrians' ability to plan ahead far enough beyond the next interaction, which explains why instead of walking away from the intruder they accept to temporarily move transversely towards denser regions on the intruder's sides. On this basis, a minimal model based on mean-field game theory proves remarkably successful in capturing the experimental observa-1
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