Hang on, I just realized there's a much simpler way to analyze the situations I described, which also works for more complicated variants like "Bob gets a 50% chance to learn the outcome, but you get a 10% chance to modify it afterward". Since money isn't created out of nothing, any such situation is a zero-sum game. Both players can easily guarantee themselves a payoff of 0 by refusing all offers. Therefore the value of the game is 0. Nash equilibrium, subgame-perfect equilibrium, no matter. Rational players don't play.
That leads to the second question: which assumptions should we relax to get a nontrivial model of a prediction market, and how do we analyze it?
The assumption you should relax is that of an objective probability. If you treat probabilities as purely subjective, and that saying that P(X)=1/3 means that my decision procedure thinks the world with not X is twice as important as the world with X, then we can make a trade.
Lets say I say P(X)=1/3 and you say P(X)=2/3, and I bet you a dollar that not X. Then I pay you a dollar in the world that I do not care about as much, and you pay me a dollar in the world that you do not care about as much. Everyone wins.
This model of probability is kind of out ther...
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.