Is there any research field dedicated to estimating a "game" itself in game theory?

Question

Game theory stuffs usually provide how a "game" works and then tries to figure out solutions - but I am wondering if there is any research field dedicated to estimating the full rules of a game. So everyone has some beliefs about how a game works, but the game has some unknown parts. But the rules of the game do not change; some of them are just unknown. Then we get sets of results as the game is played out by plaers. So is there any field dedicated to estimating the unknown rules of the game using data available...?

Edit: What I meant above is that there are only some finite and fixed possible beliefs. That means that we can form a set of beliefs. So even in this case there are no dedicated research fields?

Answer 1

There are some games whose purpose is for the players to determine the rules. The most famous is Eleusis, popularized by Martin Gardner. Others include Mao, and related ones can be found in the links on those pages.

As far as I know there has been no serious attempt to study such games, in part because their complexity is bounded only by the imagination of their players.

Answer 2

There is the field of Structural and Empirical Industrial Organisation dedicated to this. It is theoretically, statistically, and computationally intensive field that is well developed and mature, with its own distinct intellectual culture. Here is a good survey.

Answer 3

I would think that when authorities (or their advisors) are looking to detect collusion in auctions or markets or insider trading in financial markets, they are effectively testing whether the rules (they lay down) are also the rules as used by the participants (or the other way around, which statistically may be a subtly different question).

Maybe I'll add some references later, but anyone's Googling is as good as mine in this case.