[AaronBrown]

You are correct that there is no obvious mathematical solution in this case. John Nash won a Nobel prize (despite being insane) for coming up with the most common solution in this case, it's called the Nash Equilibrium. Although mathematical economists love Nash Equilibria, it's not a useful idea for poker (or much else outside of ivory tower economics).

To simplify your situation, you can construct hands where if you player A does something different than he would do if he knew all the cards, and player B does something different, you are worse off than if both players had played perfectly.

Outside of pure theory, this does happen. If you read Frank Wallace's extraordinary "Advanced Concepts of Poker," you see him using other players at the table. If you're one of his victims, you collect money from other players, only to deliver it to Frank. You can induce errors in other players, say getting them to put too much money in the pot when you have a better hand, only to find that Frank has a better hand than either of you. Or you can get them to fold the best hand, so Frank can win with the second-best hand.

I think this kind of analysis is the interesting part of poker, rather than the two-player/one-hand analysis that you read so much about.