Centipede Game, explained.
The Centipede Game is a sequential game in which passing can enlarge the available pot, while either player can stop at their turn and take the specified allocation.
Why it happens
Backward induction starts at the final decision and reasons toward the beginning. Under particular payoff and knowledge assumptions it can recommend stopping early, even though mutual passing could create larger joint rewards.
The centipede game makes the tension between immediate advantage and mutually growing gains visible one move at a time.
Read the result
Compare the current take payoff with the possible payoff after passing and the opponent's chance of continuing. The bot's programmed continuation rule is different from assuming a fully rational opponent throughout.
A worked example
A growing shared opportunity
Two partners alternate decisions about whether to take the current allocation or let the opportunity grow.
Passing creates a larger pot but also lets the other partner choose whether you get another turn.
The attraction of continued growth competes with the risk that someone stops before your hoped-for payoff.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
The initial pot is 4 and doubles after each pass. Taking pays the mover 80% and the other player 20%. The opponent independently passes at the chosen probability. A user pass prompts one opponent choice; at the final permitted decision the active player takes automatically. The plot compares pot size and the payoff for taking at each node.
Where this idea is useful
A practical use
In a collaboration, each side may want the other to make one more investment while retaining the option to claim the current return.
A common misconception
“A larger future pot makes passing automatically best.”
Your future share depends on future choices by both players. The total alone does not determine your expected payoff.
What this explanation leaves out
- The partner is a fixed stochastic policy, not a strategic learner. This short game is a teaching variant of a broader family of centipede payoff schedules.
Why might people pass in experiments?
People may value cooperation, expect different reasoning, learn through play, or doubt the assumptions of backward induction. The theoretical prediction and observed choices are distinct objects.
What must you believe about the next player for passing to be worthwhile?
Further reading
Explore the original research or the teaching reference behind this experiment.