I was wondering what are some proposed solutions in the literature to the following, well-known paradox:
Say two rational, intelligent players A and B stand in front of a stack of 100 coins, and play the following game: each turn, a player may choose to pick up one coin, giving the other player the next turn, or picking up 2 coins and ending the game right there. A and B both want to maximise their profit. They cannot talk to each other or interact in any way (outside the game itself, of course).
A might reason as follows: if we have only 2 coins, I'll pick 2 coins right there and end the game. But B, who is aware of this, will then opt to pick up 2 coins when 3 are remaining (because he'd then end up with 1 coin extra). Continuing on with this induction, we eventually arrive at the conclusion that the most rational behaviour is to pick up two coins on A's first turn. Obviously a very unusual conclusion.
(I have marked this question 'epistemology' because of ties with the "Unexpected hanging paradox")