An ant outside any shadow can see both light sources.
An ant in a non-overlapping shadow cast from one object will have one light source blocked out but the other light source will be visible to the ant.
An ant in overlapping shadows from two objects will have both light sources blocked out. (Geometrically in this case it is necessary the overlapping shadows be cast from two separated points each from distinct light sources)
When one light source is visible to the ant that area must be lighter than when no sources are visible. This is the scenario presented by the OP.
edit: Since people seem to not believe this you can find a representation in part E in this diagram
https://i.imgur.com/r6x6QPQ.jpeg
and a photograph of this nicely done with colored lights here
otikik pointed out a case of multiple light sources where overlapping shadows will be darker (otikik is correct)
fregus says "that's not correct" and argues a true case (shadows from one light source will not be darker) which is a bad argument because it tries to overgeneralize. The case from fregus is for the same light source and they cannot use this to argue otikik is incorrect because otikik's argument explicitly requires multiple light sources.
I point out, responding to fregus, how otikik is correct and how you need to consider multiple sources as well as including examples and physical evidence.
You question my reading comprehension for some reason
@fregus explicitly described a scene with two light sources. Thus the question about your reading comprehension.
They actually reference two light sources TWICE in their comment: ("any two shadows, one from each light", "from light A and in shadow from light B"). Hence the question of reading comprehension.
I think "overlapping shadows get darker" is just not a very intuitive way to think about it because it disregards the stuff that actually matters, which is the light sources and how the scene may block their light paths.
For early games that could not afford advanced methods of global illumination, making overlapping shadows get darker seems like a reasonable, though not necessarily correct, way of faking it.
And the other thing ignored in these comments is perception. For the case of the two businessmen looking at their shadows under a bridge, it is easy to show with a diagram that some areas of overlapping shadows are, in fact, darker. But in such a poorly lit scene, people are likely to conclude that there is no difference, which isn't to say that there isn't one but, rather, that they don't perceive one.