Centipede Game Explained - Why Backward Induction Says Take Immediately

The setup

4 pounds sits on the table, 3 on Ann's side. Ann can take her 3 or pass; each pass doubles the pot and hands the choice across. Six rounds, ending at 256 if everyone passes. Whoever takes gets the larger share. What does theory predict?

Short answer: Backward induction unravels every pass: the last mover would take, so the one before takes first, all the way back - Ann takes the 3 immediately.

Start at the end

At the final decision the mover chooses between taking the large share now and letting the game end with the smaller one. They take. Step one round earlier: the mover there knows the next player will take, so passing hands away the larger share - they take too.

Every rung of the ladder collapses the same way. The only subgame-perfect outcome is that Ann takes on move one and pockets 3, with 253 pounds of potential surplus never created.

What the unravelling is really telling you

The result is not a claim that people are grabby; it is a stress test of common knowledge of rationality. The chain only collapses if Ann knows Ben is rational, knows that Ben knows she is, and so on six levels deep.

In experiments people pass for several rounds and take somewhere in the middle - a little doubt about the other player, or a little willingness to gamble on cooperation, is enough to keep the pot growing for a while. Small deviations from perfect rationality are worth real money here, which is the interesting part.

Why interviews ask it

Interviewers want the clean unravelling argument stated confidently, then the acknowledgment that observed play differs and why. It is a test of whether you treat models as tools rather than as facts.