The Centipede Game

In the centipede game, two players take turns deciding whether to "take" a growing pot of money or "pass" it to the other player, with the pot doubling (or growing by some fixed amount) each round it's passed. A simple version: the pot starts at $2, and each player can grab it, ending the game and keeping the larger share, or pass, growing the pot for the next player. If both players always pass, the pot keeps growing for, say, 6 rounds, after which it's split and both do far better than if either had grabbed early.

Backward induction — reasoning from the last possible move backward — says the last player should always grab, since there's no future round left to protect. Knowing this, the second-to-last player should grab one round earlier, since passing only hands the opponent an incentive to take everything. This logic unravels all the way to the first move: the game-theoretically "rational" prediction is that the very first player takes the tiny initial pot immediately, even though both players would clearly be better off cooperating and passing several rounds.

In real experiments and in interview settings, almost nobody actually plays this way — most people pass for several rounds before someone grabs, earning far more than the backward-induction prediction. This is one of the most famous demonstrations that pure game-theoretic rationality (assuming everyone perfectly reasons about everyone else's perfect reasoning, all the way down) can predict outcomes that don't match how real people, including sophisticated traders, actually behave.