A signalling explanation might explain this behavior: people would rather be seen as having gotten the problem correct, or signal non-greediness, than get an extra $0.25. As evidence for this conclusion, some people turn down the $1.00 in box one.

No one's given the real correct solution, which is "inspect the boxes more thoroughly". One of them has an extra label on the bottom, offering an extra $1.00 for finding it if you haven't opened any boxes yet, which I've never had to pay out on. The moral is supposed to be that theory is hard to transfer into the real world and to question assumptions.