Dorm rooms, however, are so small that they have very low reverberation times (which depends on the total volume and total absorption of the room). Adding more absorption is unlikely to lower that time very much - it may not even be audible. Therefore, it won't do much to help.
Also, most affordable wall treatments like those used in recording studios are totally incorrect for a dormitory, which is a completely different occupancy classification under the building code and must be much more fireproof. Foam and most carpets burn really well. No one cares if you burn down your own home studio - but in an multi-story residential or assembly space ends up with the Station Nightclub Fire.
You are right about blocking the sound getting through. Sealing the door and windows with a heavy material could help stop sound leaks - places where the vibrating air gets in. A rug in his room won't help much, but one in his upstairs neighbors room could help soften impact noise transmitted through the structure.
There are basically two ways airborne sound travels between two rooms: 1) air leaks between the rooms. 2) through a mechanism where the sound wiggles the wall surface on one side, which wiggles the surface on the other side and re-transmits the sound back into the air.
You can stop air leaks with attention to detail during construction - the partitions should go all the way up to the ceiling, and the floor and ceiling joints should be caulked. The only way to stop the second problem is making the wall more difficult to wiggle - or increasing it's mass. Most modern dormitories have moved away from concrete and concrete block construction which is much better at stopping sound to a gypsum wall board on metal stud construction, which is lighter and therefore transmits sound much better.
Unless you want to pour a new 6" concrete wall or line the room in thick lead, you are unlikely to be able to stop the sound transmission. Having maintenance seal the door and windows better may help if there is a leak problem. You can tell by listening around the door. If the sound is much louder near the bottom of the door than elsewhere in the room, you've found the leak.
The best way to approach this problem is to go to audiologist and get fitted for custom earplugs. They will make a mold of your ear and send it to a company like http://www.etymotic.com/hp/erme.html. You can select the filter up to a maximum of -25dB over a much more even bandwidth than cheap earplugs. It will likely solve the problem without introducing masking noise willy-nilly.
That being said, a loudspeaker playing white or pink noise could mask the problem, if you don't mind listening to it. I dislike constant noise, but that would be up to you.
If you're hearing "thumping" of footsteps or feeling the noise problem, that's a different ballgame: structure borne transmission. Buy your upstairs neighbors a thick rug so they don't impact the floor as hard or replace the ceiling with something more rigid...
Computer programmers do it byte by byte.