The centipede game is a two-player finite game in which the players alternately choose either to stop or to continue. Continuing increases the total available payoff but transfers the option to stop to the other player; each player slightly prefers stopping now to having the opponent stop on the next move.
Backward induction selects stopping at the first move as the unique subgame-perfect equilibrium, even though both players receive more if play continues for many rounds. This tension has made the game a standard test of backward induction and experimentally observed cooperation.
