Interesting. There's a paradox involving a game in which players successively take a single coin from a large pile of coins. At any time a player may choose instead to take two coins, at which point the game ends and all further coins are lost. You can prove by induction that if both players are perfectly selfish, they will take two coins on their first move, no matter how large the pile is.

I'm pretty sure this proof only works if the coins are denominated in utilons.