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So do the E[X|B] bets just get cancelled if A wins? I feel like there are some unrecouped costs there, and a very real risk that manipulative bets on losing alternatives wouldn't be punished.
Easy answer, but really you should learn to solve these puzzles yourself, it's important and way below your pay grade to prove there is no market equilibrium with profit-seeking agents where a "manipulative bet" sets the price of a losing outcome.
There's a whole mathematical formalism here that I've just never had occasion to learn, I think. But I'm quite surprised that there's not some way to exploit the possibility of manipulative bets that are capable of *canceling* all payouts on the bet itself. What averts that?
It is a field (mechanism design, auction theory, etc) but this is a very basic application. 15-30 min proving the 2nd price auction result and reading examples of using no-arbitrage condition, and you could prove that a manipulated outcome is not an equilibrium.
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