Game theory would be solved if there were a set of reasonable criteria which, if applied to every possible game of rational players, would cause you to know what the players would do.
To continue with physics: physics would be solved if there were a set of reasonable criteria which, if applied to every possible interaction of particles, would cause you to know what the particles would do.
Consider a situation in which using physics you could prove that (1) X won't happen, and (2) X will happen. If this situation existed physics wouldn't be capable of being solved, but my understanding of science is that such a situation is unlikely to exist. Alas, this kind of situation does come up in game theory.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.