Game Theory · GT-16
Backward induction says grab the small early payoff immediately — real players keep cooperating far longer than theory predicts.
A sequential game where two players alternate choosing to 'take' a growing pot (ending the game) or 'pass' (growing the pot further, handing the choice to the other player). Backward induction predicts the first player should take immediately — yet real players consistently pass many rounds before taking, earning more than the theoretical prediction.
Introduced by Robert Rosenthal in a 1981 paper; named for the game tree's many-legged, segmented visual shape once diagrammed out over many rounds.
The Mechanism
The unraveling nobody actually follows
Real experimental play consistently passes several rounds before someone finally takes — the theoretical unraveling is logically airtight but empirically almost never observed in its purest form, one of the starkest gaps between game theory's predictions and lab behavior.
01 · BACKWARD INDUCTION'S LOGIC IS AIRTIGHT — AND STILL WRONG EMPIRICALLY
A genuine puzzle for rational-choice theory
If both players are certain the other is a strict payoff-maximizer, the entire game unravels to an immediate take at move one, regardless of how large the eventual pot could grow. Experimental economics (starting with McKelvey and Palfrey's influential 1992 study) consistently finds real players pass for several rounds, defying the theoretical prediction in a way that's proven remarkably robust to replication.
02 · UNCERTAINTY ABOUT THE OTHER PLAYER'S TYPE EXPLAINS MOST OF THE GAP
Not full irrationality — rational response to doubt
If a player assigns even a small probability that their opponent isn't a strict payoff-maximizer (might be an 'altruist' type who always passes), it becomes individually rational to pass longer than pure backward induction predicts — this 'reputation' logic (formalized in models building on Kreps-Wilson-style reasoning) explains a meaningful share, though not all, of the observed gap.
03 · IT'S A CAUTIONARY TALE ABOUT OVER-TRUSTING BACKWARD INDUCTION
Real behavior systematically outperforms the 'rational' prediction
The Centipede Game is frequently cited specifically as a warning against treating multi-step backward-induction predictions as reliable behavioral forecasts — the logic can be flawless while still badly mispredicting what real, only-partly-strategic humans actually do.
Where It Fails / Inversion
Where it fails / inversion
Trusting backward induction too literally in any long, multi-round negotiation or relationship can lead you to defect or 'take' far too early — sacrificing the much larger value both sides could have realized by continuing to cooperate, purely because a theoretically airtight argument said the other side would eventually defect anyway.
How To Use It
Worked example · long-term joint ventures with an eventual known end date
Two companies in a multi-year joint venture with a known contract expiration can, in principle, backward-induct their way to defecting early, each anticipating the other's eventual defection near the end. In practice — mirroring Centipede Game findings — most real joint ventures sustain cooperation well past the point pure theory predicts they should unravel, because reputational stakes, uncertainty about the partner's true type, and the sheer cost of being wrong about early defection all favor continuing to cooperate longer than the airtight logic suggests.
How to use it
Don't let a clean backward-induction argument talk you into defecting early in a valuable ongoing relationship just because the relationship has a known endpoint. Real cooperative equilibria in these games typically survive much longer than the theoretical unraveling predicts — the theory is a useful worst-case bound, not a forecast of what will actually happen.
See Also