Do pilots ever increase the cabin altitude intentionally?
I've never heard of this "trick" being used or recommended, although the limits of what I've heard are pretty much limited to US commercial aviation.

If you climb the cabin from the usual 8000' to 10,000', the incremental gain in "sleepy" factor is a little bit but not all that much.  If you climb it above 10,000', then you might "encourage" a few of the more tired/drunk/elderly folks to go to sleep, but now you're into the realm of operating outside of normal practices, and you need to start considering things like, the pilots both need to be on oxygen, the flight attendants may get "tired" quicker than the passengers do, anybody who is elderly or in poor health may start suffering consequences, and then there are company policies and national regulations to consider.

If you raise the cabin above about 14,000 - 15,000' depending on your specific aircraft, then you'll end up activating the automatic passenger oxygen masks, and now you've got some serious 'splainin to do!  (#1, it's a bunch of work for maintenance to repack them, and the aircraft is grounded until they do, and #2 you open yourself up to all sorts of issues if you still have a long way to fly at high altitude to get to your destination!)

I'm going to guess that in the history of aviation, this sort of trick probably has been used at some point, but the opportunity for the uncomfortable questions along the lines of, "okay, tell me again, you did what exactly???" to which the best available answer is along the lines of, "um, well, it, ah, seemed like a good idea at the time, sir..." is awfully high.

I certainly wouldn't recommend it.