Sure, I didn't go far into detail, but it's actually worse than either of us has said because once B surrenders anything ($1 or $1,000,000,000), they are at eve

Sure, I didn't go far into detail, but it's actually worse than either of us has said because once B surrenders anything ($1 or $1,000,000,000), they are at even greater disadvantage and "logically" should surrender more money. In fact, they should surrender the entire country, as once they are at a disadvantage A can keep coming back forever. Effectively, the idea that war would not happen with perfect information suggests that the logical thing to do is for all countries to surrender control to the strongest country immediately.