The Centipede Game

Game Theory · Axiom Academy

1. The Centipede Game Structure Two players alternate choosing between Stop and Continue . The game has a finite number of decision points (typically 4-6). At each stage, the current player can either: Stop: End the game and receive the current payoffs Continue: Pass control to the other player, increasing the total pot Key feature: Each time a player chooses Continue, both players' potential payoffs increase, but the player who Stops gets a slightly larger share. 2. Backward Induction Analysis Using backward induction, we analyze the game from the final decision point backward to the start: At the final node: The last player will always choose Stop (gets higher payoff than letting the game end automatically). One step earlier: Knowing the opponent will stop at the final node, the penultimate player should stop now rather than continue. Continuing backward: This logic cascades all the way back to the very first decision. Here's the paradox: backward induction predicts immediate defection, but this leads to minimal payoffs for both players. If both players cooperate for several rounds, they both earn substantially more. Theoretical prediction: Stop at move 1 Observed behavior: Players typically continue for 2-4 rounds before stopping Common knowledge assumptions: Backward induction requires perfect rationality and common knowledge thereof Altruism and fairness: Players may care about joint payoffs or fairness Uncertainty: Players may be uncertain about opponent rationality

This is the written version of the interactive lesson above. See the full Game Theory course.