Centipede Game
A multi-stage game where backward induction predicts immediate termination despite cooperative gains.
Definition
Players alternate; at each node a player can Take (ending the game) or Pass. Taking earlier yields a larger share; the pot grows if both Pass.
Backward induction: the last mover Takes, so the previous mover Takes, unraveling back to the first node.
Intuition
Rational backward induction predicts immediate Take; experiments show extensive cooperation until near the end.
Challenges the plausibility of common knowledge of rationality in long chains.
Worked example
McKelvey-Palfrey (1992) found roughly half of subjects continued past the midpoint, contradicting the SPE prediction.
Rosenthal's original centipede has rapidly escalating payoffs making the paradox sharp.
The math
SPE is the unique backward-induction outcome; level- and quantal-response models rationalize observed behavior.
Epistemic analyses show that -fold common knowledge of rationality fails at long horizons.
Where it is used
Teaches the empirical limits of backward induction and motivates bounded-rationality refinements.
Widely used in experimental economics labs.
More in Game theory
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