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Interacting with humans remains a challenge for autonomousvehicles (AVs). When a pedestrian wishes to cross the road in front of thevehicle at an unmarked crossing, the pedestrian and AV must competefor the space, which may be considered as a game-theoretic interaction inwhich one agent must yield to the other. To inform development of newreal-time AV controllers in this setting, this study collects and analy-ses detailed, manually-annotated, temporal data from real-world humanroad crossings as they interact with manual drive vehicles. It studies thetemporal orderings (filtrations) in which features are revealed to the ve-hicle and their informativeness over time. It presents a new frameworksuggesting how optimal stopping controllers may then use such data toenable an AV to decide when to act (by speeding up, slowing down, orotherwise signalling intent to the pedestrian) or alternatively, to continueat its current speed in order to gather additional information from newfeatures, including signals from that pedestrian, before acting itself.