Why the Centipede Game Can End Too Soon
The Centipede Game is a turn-taking contest in which two players can either take the money available now or pass, letting the pot grow before the other player gets a turn. Taking ends the game and gives the taker more than the other player; passing creates the possibility of a larger reward for both, but leaves the next move—and the larger immediate prize—in the opponent’s hands.
That tradeoff makes the game a test of backward induction: solving a problem by starting at its final decision and reasoning toward the present. At the last turn, there is no future opportunity to earn more by passing, so the final player should take. The player just before that can anticipate the final player’s choice and take first. Repeating this logic moves the predicted stopping point backward, potentially all the way to the opening move.
Individually Sensible, Collectively Costly
The result is not that a player makes a mathematical mistake. It is that the reasoning focuses on what each person can secure, not on what the pair could earn by continuing. Passing may increase the total available, but it also gives the other player a chance to end the game and claim the better share. If both follow the backward logic, neither needs to trust the other enough to keep the pot growing.
That is why the game’s outcome can look paradoxical: a chain of choices that each player can justify on their own can leave both with less than they might have received through continued cooperation. In real play, people may pass because they expect reciprocity, value fairness, or hope for a larger joint payoff. But every pass also makes the next player’s temptation to take more immediate. The pot grows one turn at a time; so does the risk that cooperation will stop.
