What is this addictive game structure called?

(Disclaimer: I work in the game industry, but production not design) This is very bedrock Design 101 stuff, and really it's all based off of a http://en.wikipedia.org/wiki/Skinner_box. Play WOW for a couple hours, you get a carrot in the form of a new spell, an upgraded spell, a new piece of equipment, etc. It's really straightforward conditioning, and it works well. Toss in a social element (personal narrative and drama) to keep people distracted from the nature of the system (special sequences and events contribute to this while doubling as a different type of carrot) if they're going to be playing for an exceptionally long time. Games in general are pretty addictive more as a byproduct of the need to 'ramp up' players than anything else. MMOs however are directly designed to be as addictive as possible with an eye towards long-term viability. Many companies producing the latter heavily research the psychology of addiction and intentionally exploit it in an effort to retain players. This is why most MMOs follow a social/adventure model (EQ, DAOC, WOW), rather than an open-ended simulation model (old-school Ultima Online).

You might take a look at books by the psychologist http://en.wikipedia.org/wiki/Mihaly_Csikszentmihalyi. He has spent his life writing about the concept of flow:Flow occurs in an existential middle ground. We experience it when a balance is achieved between abilities and responsibilities, when the skills we possess are roughly commensurate with the challenges we face, when our talents are neither underused nor overtaxed. Flow emerges in circumstances that are perceived as both problematic and soluble. from http://www.google.ca/books?id=lNt6bdfoyxQC&pg=PA3&ots=k6Pylqg0Cg&dq=Mih%C3%A1ly+Cs%C3%ADkszentmih%C3%A1lyi&sig=ddYNuUCl4t8G9XYeuILl-9MaZGY#PPP1,M1Edited by Mihaly Csikszentmihalyi, Isabella Selega Csikszentmihalyi In particular, you should check out http://www.amazon.com/exec/obidos/ASIN/0060920432/metafilter-20/ref=nosim/ and http://www.amazon.com/exec/obidos/ASIN/0465024114/metafilter-20/ref=nosim/. In particular, Finding Flow has many suggestions for structuring your everyday life so you’re more likely to experience feelings of flow. You should be able to incorporate these ideas in your classroom.

In anime it's known as the "http://tvtropes.org/pmwiki/pmwiki.php/Main/SortingAlgorithmOfEvil".

For the record, I don't see this in Settlers Of Catan, but if you're interested in seeing it implemented in an excellent board game, try Power Grid. The power plants at the beginning of the game are limited, inefficient, and expensive to run. As the game goes on, new power plants become available, and though these are more powerful and more efficient, your needs are greater, too. Power Grid is currently number 3 on the Board Game Geek rankings. Number 1, Puerto Rico, has a bit of this quality as well--as the game goes on, you have more money with which to buy buildings with more powerful abilities--but the phenomenom you've described is really evident in Power Grid. (Plus it's super-fun...I don't know what grade you teach, but it's suitable for your typical seventh or eighth-grader.) If you're interested in other board games that use the same mechanic, post a question on the Board Game Geek forums...by tomorrow afternoon you'll have hundreds of examples.

...and/or possessing "skill trees" as suggested above.

I think the general psychological term is http://en.wikipedia.org/wiki/Reinforcement: simple positive reinforcement rewards achievement. By keeping the reward (here's a new spell, bigger sword, etc) small (there's alway another challenge ahead), it prevents the player from becoming bored. For real addiction, partial negative reinforcement is the way to go: the player usually loses, but wins just often enough to want to stay in the game. It's the principal draw of gambling. That said, my experience with RPGs is that advancement is largely illusion. Sure, now you've got more hit points and a bigger sword, but now the monsters are bigger as well. I'm not sure that this is true in the classroom; some subjects really do get harder faster than the students can "level up."

This may be a stupid answer, but back when I used to play such things, we just referred to them having a tiered (skill) system.

I'd disagree about the Power Grid reference. Power Grid's power plants change in numerical function, but they don't actually represent shifts in rules like, say, flight or gunpowder do in Civilization. The person who really gets this stuff and is applying it directly to education is Katie Salen. She's starting the http://www.instituteofplay.com/, about which I am rather obsessed. I really hope she does well because I - like you - see tremendous potential in techniques like this. I don't think anyone has really nailed it yet, but if anyone's going to it's Katie Salen.

This sounds like the 'reading tree' we had in third (?) grade, with like 50 books on it, along with certain prizes in strategic places. Books had to be read and reported upon before one could move further up the branch, and there was a choose-your-own-adventure quality to making decisions about which path to follow. If I want a yo-yo, I'll go that way and read those two books... or maybe I'll change my mind and go for the superball. The prizes were dime-store type, but enough to make it interesting. Even the books seemed to be carefully positioned: the coolest books always required reading the most boring first. I imagine they were also in ascending difficulty, but I wasn't clever enough to notice that then. In retrospect, I admire the engineering that must have went into planning that tree. But at the time, I just wanted the damn magic flashlight.