The centipede game is a sequential Game Theory model where two players alternate choosing whether to take a growing payoff or pass the move. It shows how backward induction can predict early stopping even when both players could earn more by continuing.
The centipede game is a sequential game in Game Theory where two players take turns deciding whether to take a payoff or pass the decision to the other player. Each time a player passes, the total possible payoff usually gets larger, but the chance of losing it also grows. That setup makes the game a clean example of strategic reasoning under uncertainty about the other player’s choices.
The name comes from the game tree, which often looks like a centipede with many “legs,” or decision points. At each stage, one player can grab a larger share for themselves or let the game continue. If both players keep passing, the potential payoff increases over several rounds. If one player takes, the game ends immediately and the money is split according to that stage’s rules.
What makes the centipede game famous is the tension between individual incentive and mutual gain. If you look only at the final move, the last player should take the money rather than pass, because there is no future round to benefit from. Backward induction then pushes that logic earlier and earlier: if the last player would take, the previous player should take first, and so on. Under that reasoning, a fully rational player may stop the game much earlier than you might expect.
That prediction is why the centipede game gets used in topics like backward induction and subgame perfect equilibrium. It is a sequential game with perfect information, so both players can see the history of play and reason about what comes next. The model is simple, but it exposes a real problem in strategic thinking: people often care about fairness, trust, or future cooperation, not just the payoff from the current move.
In experiments, many players pass longer than backward induction predicts. That does not mean the model is useless. It means the centipede game is a sharp way to compare idealized rational choice with actual human behavior. When a class discusses why people cooperate, hesitate, or keep trusting an opponent, this game is one of the clearest examples.
The centipede game matters because it shows how Game Theory handles sequential decisions, not just one-shot choices. A lot of classic games focus on picking a strategy all at once, but the centipede game forces you to think about what happens after each move and how later choices change earlier ones.
It also gives you a concrete way to use backward induction. Instead of memorizing the phrase, you can trace the logic step by step: if the last mover would take, then the previous mover should also take, and the reasoning continues backward to the start. That makes it one of the best examples for explaining why subgame perfect equilibrium can differ from what feels cooperative or fair.
The term is also useful because it shows the limits of pure payoff maximization. Real players often pass longer than theory predicts, which opens the door to talking about trust, communication, social preferences, and bounded rationality. If your class discusses why experimental results sometimes differ from game-theoretic predictions, the centipede game gives you a clear case to cite.
In economics, politics, or social interaction examples, the centipede game can model any situation where people can stop early for a safe gain or continue for a potentially better shared outcome. That makes it a useful bridge between formal game trees and real behavior.
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Visual cheatsheet
view galleryBackward Induction
Backward induction is the solving method behind the centipede game. You start at the final decision node, figure out what the rational move would be there, and then work backward to earlier moves. In the centipede game, that logic often leads to an early take, even though passing could increase the total payoff.
Subgame Perfect Equilibrium
The centipede game is a classic way to find subgame perfect equilibrium in a sequential game. The equilibrium has to make sense not just at the start, but after every possible decision point. That is why the game is useful for showing how a strategy can be consistent in every subgame and still feel counterintuitive.
Nash Equilibrium
A Nash equilibrium only requires that no player wants to change their strategy given the other player’s strategy. In the centipede game, that idea is not enough by itself to explain the full step-by-step logic of play. The game helps you see why Game Theory often prefers a stronger concept, like subgame perfect equilibrium, in sequential settings.
first-mover advantage
The centipede game can show a first-mover advantage if the first player can force an earlier end and secure a payoff before the other player does. But that advantage depends on how the game tree is structured and what both players believe about future moves. It is a good example of how being first can change the bargaining position.
A problem set or quiz item on the centipede game usually asks you to trace the game tree, identify the payoff at each decision node, and apply backward induction to predict the outcome. You may also need to explain why the backward-induction prediction says the game ends early, even though later passes create higher total payoffs.
If the instructor gives you an experimental result or a class discussion prompt, you can use the centipede game to compare rational-choice theory with actual behavior. A strong answer usually names the equilibrium idea, then points out the gap between prediction and what people often do in lab settings. If communication or trust is added to the story, mention how those factors can lengthen play.
The centipede game is a sequential Game Theory model where players alternately choose to take a payoff or pass the move.
Backward induction often predicts that rational players will stop early, even when waiting could create a larger payoff for both players.
The game is a standard example of subgame perfect equilibrium because each move has to make sense from every later decision point.
Experiments often show players passing longer than theory predicts, which brings trust, fairness, and social preferences into the analysis.
The centipede game is useful anytime you need to explain why strategic reasoning can be very different from real human behavior.
The centipede game is a sequential game where two players take turns deciding whether to take a payoff or pass to the other player. Passing usually increases the possible payoff, but it also keeps the risk alive. Game Theory uses it to show how backward induction works in games with perfect information.
Backward induction starts at the last move and asks what the rational choice is there. If the last player should take, then the previous player should also take, because passing just hands over the same incentive one step later. Repeating that logic pushes the decision all the way back to the beginning.
No. The Prisoner's Dilemma is usually a simultaneous-move game, while the centipede game is sequential and uses alternating turns. Both can show a gap between self-interest and mutual benefit, but the reasoning tools are different because one depends on timing and the other on simultaneous choice.
You usually solve it by drawing or reading the game tree, then applying backward induction from the final node to the first. After that, you identify the predicted equilibrium path and explain why the chosen action at each step is the best response. Some classes also ask you to compare the prediction with experimental behavior.