Propeties the model should have:
- Well motivated: the game is actually is a plausible model of a real world situation. Maybe with some parameters learnt from data.
- Complete: it is a complete game theory model. This will probably using a Harsanyi-style completion to form the imperfect information game.
- Asymmetric information is important. Players have private information and deducing the information of other players is important to the strategy of the game.
- Complex enough: so that it can't be analysed with pen and paper. But not so complex that coding up a simulation would be difficult.
(Note that poker has all the properties except the first.)
The reason I ask is that there has been a lot of progress on poker by participants in http://www.computerpokercompetition.org/ . (I am a former participant). And there has been discussion of adding to the games played in the competition. So an economics researcher might get some quite sophisticated AI programmers to work out optimal play in their model, if they can frame it as a poker game and get it accepted into the contest.