Slightly off topic…

> Suppose two players notice each other at the same time (e.g. as would naturally happen when walking around a corner in a shooter)

This is not true for third person games. Depending on a left sided or right sided peek and your angle or approach, players see asymmetrically.

For example, Fortnite is a right side peek game. Peeking right is safer than peeking left as less of your body is exposed before your camera turns the corner.

I believe distance also plays a part in the angles.