I highly recommend Brad Plumer's article on economists studying the economies that exist inside big multiplayer video games.
There's just one thing that I want to add to the mix, namely that I really want this field to be called "fake business cycle theory." It's endlessly annoying to me that in economist-ese the opposite of "nominal" is "real" as if nominal quantities are somehow fake. Fake economies are very much a thing. They're right there in Eve Online and Second Life and the Valve and whatnot. And they have business cycles. Fake ones.