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IANAL, but this is one of those questions where you can start out by asking, are other people doing this. If not, there is a good chance that the answer is that you can't do it either. This is es...
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#4: Attribution notice removed
Source: https://writers.stackexchange.com/a/27941 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#3: Attribution notice added
Source: https://writers.stackexchange.com/a/27941 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
IANAL, but this is one of those questions where you can start out by asking, are other people doing this. If not, there is a good chance that the answer is that you can't do it either. This is essentially what is called a tie-in. Your book would be tied into the world of the games. People who play those games would be a natural market for your story. (In fact, I suspect people who play the games would be pretty much the only market.) So, your books would be profiting from Nintendo's IP and if there is a way to stop people from profiting off their IP, Nintendo would do it. From which we can reasonably (though not definitively) conclude that it someone else is doing this, then there probably nothing Nintendo can do to stop them, and if they are not doing it, that is almost certainly because there is something Nintendo can do to stop them. But don't overlook the obvious here. Instead of trying to avoid trouble with Nintendo, take the whole project the Nintendo and propose it to them. Media companies love tie-ins. It is a way to extend their brand and therefore to make more money from it. And if Nintendo likes the idea, then they will take care of the publishing process for you. If the books sell, they will probably contract you to do the same for other titles. And since game/movie tie ins are a thing (its is beyond me why, but go figure) your book might even become the basis for a movie. TL;DR: Since you almost certainly can't beat them, join them.