Who is the audience and what are the desired outcomes from playing the game?
I can guess, but it is better to outline these things explicitly at the start, lest you wind up with something that no-one wants to play.
As for genre, I immediately think of something like a role playing game. I think back to FFVIII, which allowed you gain, increasing your salary when you took in-game tests. More recent RPGs that have huge volumes of information in in-game encyclopedias (games like KOTOR 1 and 2, Mass Effect, Xenosaga, etc).
I would consider using a plot similar to the Harry Potter fanfic, such that your character starts off in a non-rational place, and advances using these techniques. Techniques and studies are mentioned in the dialogue, and full references become available in the encyclopedia as they are mentioned.
This sounds like a really interesting idea. I have always wanted to design a game. Sadly, I just don't have the time (or the knowledge).
I'm kind of wondering how exactly e.g. any online RTS game wouldn't qualify as 'rationality game' as you get trained with very clear win/lose criteria, in a situation rather reminiscent of the real world as far as the size of the problem vs the thought time is concerned, as well as handling of uncertainty (with fog of war). Unless the belief in superiority of particular set of rationality techniques got down to the dragon in the garage level where you do proclaim that those would e.g. help win a tournament at arbitrary game of wits but do not seriously expect that it would happen and do not want to spread flour in the garage to check for the invisible dragon.
Every game is a rationality game if you define rationality as "winning". We're not looking for games where it's important to your victory to be rational, we're looking for games that teach generalizable rationality skills. Starcraft teaches things like ROI and VOI implicitly, not explicitly, and in ways that aren't easy to apply to real world situations. Maybe you can make the leap from "I should make a scout because it's easy and doesn't take too many of my APM and will seriously help me win" from "I should research different colleges instead of just going to the one in my local town because the potential payoffs are huge and the costs are low." but I doubt that's the case for almost anyone who plays starcraft and it's certainly not optimized for it.
I wouldn't be surprised if playing these types of games seriously provided some benefit to general rationality, but I agree that for teaching purposes you want to be more explicit.
But are those definitely more generalizable? There's a lot of talk about 'akrasia' here. Openings in RTS games (or non-realtime strategy games like Chess) are very important and significant part of the win is that you must research different opening strategies carefully.
I've seen this argument in particular for games like chess and go. The question is how transferable this stuff is. The conventional wisdom seems to be that mastery in something like chess is mostly just learning to pattern-match situations and responses in context of chess games, and doesn't translate to more general aptitude. Though I think the non-transferability studies were about general intelligence, which is very tricky to raise. Studying the rationality skills, which are learnable, of expert go, chess or poker players might be interesting.
I wonder if the abstractness of the game matters here. Picking up analogous patterns to game situations outside the game could work, and more situations might match if the game is very abstract and bare-bones in its model, like go. The default state is probably still compartmentalization, people skilled in the game don't make an effort to unify what they learn in one domain with non-game domains.
I know there is interest among this community in building rationality oriented games as teaching tools. Today we announced Steam Greenlight. We're essentially turning the game approval process over to the community. It may be possible for quality rationality games produced by the Less Wrong community to create enough gamer-community interest to get placed on Steam for distribution.
http://steamcommunity.com/greenlight
I feel that this creates a better opportunity for rationality games as teaching tools to find broad distribution than if it had to go through the Steam product review team. Ultimately, it shifts the responsibility onto the games' creators and their community to create and drive interest for the product and it removes our limited decision making from the system.
I'm posting this here for awareness of this possible avenue toward reaching a broader audience.