On busy sidewalks with many people moving rapidly in both directions, how are collisions avoided? If two people each attempt to intuit the other's trajectory while maintaining eye contact, a game of infinitely recursing mirrors ensues, Inception-style.

What works is to pick a path, any path, and look in the direction of that path. That is a sufficient signal for all parties to self-organize and avoid collision, even at high speeds and density of people. In other words, leading lowers the cost of following.

Even if one could mind-read, one may not like what one perceives. But humans are adaptable and can often reciprocate. If one's actions assume/imply positive intent, one can motivate positive reciprocity and reduce/avoid the cost of perceiving intent.