Centipede Game

A sequential finite-horizon game in which each player can take the larger share or pass to grow the pot, where backward induction prescribes taking on the first move — isolating common knowledge of rationality as the load-bearing assumption cooperation depends on.

Core Idea

The Centipede Game (Rosenthal, 1981) is a sequential two-player game with perfect information and a known finite horizon in which cooperation unravels by backward induction despite paying more the longer it lasts. At each node a player takes (ending the game with the larger share) or passes (growing the pot and handing over the move). Backward induction prescribes taking on the first move, yet subjects routinely pass for many rounds (McKelvey and Palfrey, 1992). The gap isolates common knowledge of rationality as the load-bearing assumption.

Scope of Application

It lives across game theory wherever a situation is genuinely centipede-shaped — a sequential, perfect-information, common-knowledge finite horizon with a growing joint payoff and a known last move.

• Game theory proper — the canonical case of finite-horizon backward-induction failure.
• Behavioral economics — the standard testbed where equilibrium diverges from play.
• Bounded-rationality modeling — the proving ground for level-k and quantal-response models.
• Reputation and trust experiments — designs letting reputation accumulate across rounds.
• Finite-horizon negotiation — the unravelling of cooperation once the end-date is known.

Clarity

The game's clarifying force is that it isolates a single load-bearing assumption and makes its failure observable. Real cooperation breakdowns are overdetermined; the centipede strips away information asymmetry, coordination problems, and dominant-strategy temptation, leaving only the backward-induction chain, which rests on common knowledge of rationality. It converts an abstract worry into a replicable measurement of how far reasoning propagates, and it forces a specific reading of any observed deviation.

Manages Complexity

Cooperation breakdowns come as overdetermined messes. The centipede shuts off all but one force by design, collapsing the sprawl of candidate causes to a single isolated assumption. That imposes a clean three-branch structure on what a deviation can mean — bounded depth, belief-uncertainty, or other-regarding preferences — from which the modeller reads off the rest. The compression travels: recognizing a situation as centipede-shaped imports the whole apparatus without re-derivation.

Abstract Reasoning

It licenses backward-induction prediction folding the solution from the last node; isolation-by-design diagnosis that pins any deviation on the common-knowledge chain; three-branch attribution of an observed deviation to a testable model; and skeleton-recognition transfer that imports the apparatus to any finite-horizon cooperation and predicts that sustaining cooperation requires breaking the common-knowledge chain on purpose.

Knowledge Transfer

Within game theory the centipede transfers as model wherever a situation is genuinely centipede-shaped — the chain-store paradox, finite-horizon negotiation, finitely-repeated PD with a known endpoint — each a real instance, not a likeness. But this breadth is one substrate (reasoning agents) at many scales, not cross-domain reach; stripped of game-theoretic vocabulary it has no counterpart in chemistry or ecology. The portable content is one level up: the parent finite_horizon_unravelling, kin to backward_induction.

Relationships to Other Abstractions

Current abstraction Centipede Game Domain-specific

Parents (2) — more general patterns this builds on

• Centipede Game is part of Subgame Perfect Equilibrium Domain-specific

  The canonical centipede construction contains its subgame-perfect solution, whose every-node credibility requirement yields take on the first move.

• Centipede Game is part of Common Knowledge Prime

  The centipede model contains common knowledge of rationality and the final move as the epistemic chain that propagates backward to immediate taking.

Hierarchy paths (7) — routes to 6 parentless roots

• Centipede Game → Subgame Perfect Equilibrium → Nash Equilibrium → Equilibrium → Fixed Point

Show alternative paths (6)

Neighborhood in Abstraction Space

Centipede Game sits in a crowded region of the domain-specific corpus (1^st percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Strategic Interaction & Game Theory (23 abstractions)

Nearest neighbors

• Traveler's Dilemma — 0.90
• Folk Theorem (Repeated Games) — 0.89
• Ultimatum Game — 0.89
• Dominated Strategy — 0.89
• Guess ⅔ of the Average — 0.89

Computed from structural-signature embeddings · 2026-07-12