What it means
The game is set up as a short sequence of decisions. A small pot sits on the table, and each player in turn either takes the larger share and ends the game, or passes, which makes the pot bigger before the other player faces the same choice.
The puzzle comes from working backwards, a method called backward induction. At the final decision the player facing it does better by taking than by passing, so you assume they will take, which means the player before them does better by taking first, and that reasoning unravels all the way back to the opening move.
The prediction is therefore that the game ends immediately with a small payoff, even though a few rounds of mutual trust would leave both players much better off. That is why the game appears in discussions of trust, reputation and cooperation rather than only in mathematics.
What makes it famous is that real people do not behave as the logic predicts. In experiments most players pass at least once or twice, and many pass several times, which suggests that people factor in fairness, reputation and the chance that the other side will also cooperate.
For business, the game is a neat model for any relationship where both sides gain by continuing but either can cash out early. Supplier development, joint ventures, phased payments on a project and gradual disclosure during a negotiation all have the same shape.
The practical lesson is about changing the structure rather than preaching trust. If you want the pot to keep growing, you make the end point less visible, add repeat business so the final round never truly arrives, or write contractual penalties that make grabbing early the worse option.
In practice
Real-world examples.
Example
Two engineering firms share early design work on a bid, and each additional round of sharing improves the joint proposal. Either firm could take the combined design and bid alone, which is the take move, so they sign a short exclusivity agreement that makes the early grab expensive. The structure, not goodwill, is what keeps the pot growing.
Example
A startup negotiating with a large distributor reveals its customer data in stages. Giving everything at once would let the distributor walk away and build its own version, so each disclosure is matched by a signed commitment. Both sides end up better off than if the startup had held everything back.
Example
A manager and a supplier agree a three-year cost reduction plan where savings are shared. The supplier fears the buyer will pocket the savings and retender in year two, so the contract fixes the share for all three years. Removing the final round removes the incentive to grab early.
Formula
Calculation
At each turn: Taker's payoff = the larger share of the current pot, and Passer's payoff = the smaller share if the other player then takes. The pot grows at each pass, so the question is always whether the larger share now beats the smaller share later.
Set up a four-decision version where the pot doubles on every pass and whoever takes receives 80% of it. Player A moves first with a pot of $10, so taking gives An $8 and leaves B $2. If A passes the pot becomes $20, and if B takes, B receives $16 and A receives $4. If B passes the pot becomes $40, and if A then takes, A receives $32 and B receives $8. If A passes again the pot becomes $80, and if B takes at that final node B receives $64 and A receives $16, while if B also passes the $80 is split evenly at $40 each.
Now work backwards. At the final node B compares $64 from taking with $40 from passing and takes, so at the third node A compares $32 from taking with the $16 that passing would leave, and takes. At the second node B compares $16 from taking with the $8 that passing would leave, and takes, so at the first node A compares $8 from taking with the $4 that passing would leave, and takes. The logical result is that A ends the game at once for $8 while $40 each was available, which is the whole point of the puzzle.Case study
Seen in the real world.
Pelleray Instruments and Sorne Optics are illustrative, entirely fictional companies used here to walk through the game. They agree to co-develop a sensor, with each stage of shared research making the eventual product more valuable, and the first prototype is worth about $10,000,000 if either partner commercialises it alone.
Sorne's commercial director notices that whoever stops cooperating first and files the patent captures roughly 80% of the value at that moment. She raises it at a steering meeting: by the logic of the centipede game, both sides should expect the other to defect, which would freeze the project at its least valuable stage.
The partners respond by rewriting the agreement rather than exchanging reassurances. Joint patents, staged milestone payments and a five-year revenue share remove the final round entirely, and the illustrative project runs to completion with a product worth several times the early prototype.
Watch out
Common mistakes.
- Reading the game as proof that people are purely selfish, when experiments consistently show players passing far longer than the logic predicts.
- Assuming backward induction always describes real behaviour, when it depends on both sides being certain the other is perfectly self-interested.
- Thinking the game needs a hundred rounds because of the name, when most versions used in teaching have only four to six decisions.
Questions
People also ask.
Why is it called a centipede?
Because the decision tree drawn out looks like a long body with a short leg hanging off at each decision point.
What does it teach a manager?
That cooperation usually needs structure, such as repeat business or contractual penalties, rather than an appeal to good faith.
How is it different from the prisoner's dilemma?
Players move in turn rather than at the same time, and the total prize grows with each round of cooperation.
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