Often, they "speed" to a much greater degree than the "speeders" they go after – in order to catch up with them. And – sometimes – they incite the "speeder" to make an attempt to get away from them, for the same natural reason any prey animal with an instinct for self-preservation will "attempt to elude" a predator.

A video of such an incident was forwarded to me by a friend. It is of interest because it's not often you can actually see cognitive dissonance in action.