The centipede game is a sequential game in Intermediate Microeconomic Theory where two players alternate choosing to pass or take an enlarging payoff. It shows how backward induction and subgame perfect equilibrium can predict early stopping.
The centipede game is a sequential game in Intermediate Microeconomic Theory where two players take turns choosing whether to pass the move or take the payoff at that stage. As the game moves forward, the possible payoff gets larger, so passing can create a better outcome later, but only if the other player keeps passing too.
The setup looks simple, but that is exactly why it shows up in game theory. Each player has to think about what the other player will do next, not just what is available right now. If you are analyzing the game as a game tree, every decision node gives the current player a choice between a smaller certain gain now and the chance of a larger gain later.
The standard theory prediction comes from backward induction. You start at the last decision and reason that the last player would take the payoff instead of passing, because passing would only leave them worse off or no better off. Once you accept that last move, the previous player knows the next player will not pass, so the previous player should take earlier, and so on until the game ends immediately.
That logic leads to the subgame perfect equilibrium outcome, which is usually the earliest possible take. The surprising part is that this is not the same as the outcome that maximizes the combined payoffs over the whole path. The players could both do better if they trusted each other to keep passing for a few rounds, but the game structure makes that cooperation fragile.
This is why the centipede game is such a useful classroom example. It shows how sequential rationality can produce a noncooperative result even when later outcomes look better on paper. It also gives you a clean way to see the gap between the purely strategic prediction of a model and what real people sometimes do in experiments.
In practice, experimental players often pass more than backward induction predicts. That does not mean the model is useless. It means the centipede game gives economists a sharp example for studying trust, beliefs about other players, and why people may not always follow the strict equilibrium path.
The centipede game matters because it is one of the clearest examples of how sequential games differ from simultaneous-move games. In Intermediate Microeconomic Theory, you are not just asking whether a strategy is best in isolation, you are asking what happens when each move reveals information and changes the other player’s next decision.
It is also a clean test case for backward induction. If you can work through why the last mover takes, then why the previous mover takes, you are using the same logic that shows up in many subgame perfect equilibrium problems. That skill carries over to bargaining, entry deterrence, auctions with stages, and any model where timing matters.
The game also helps you see why equilibrium predictions can feel counterintuitive. A purely self-interested solution says stop early, but a more trusting or cooperative path can produce higher joint payoffs. That tension is useful when you are comparing theoretical outcomes with experimental results or with real business situations where firms care about reputation and future interaction.
When you study this term, you are really practicing how to read strategic incentives step by step, instead of just naming the equilibrium. That is a core micro skill.
Keep studying Intermediate Microeconomic Theory Unit 11
Visual cheatsheet
view galleryBackward Induction
Backward induction is the method used to solve the centipede game. You reason from the final move back to the first move, asking what a rational player would do at each point if they know the later action. In this game, that logic predicts early taking, even when later payoffs look better.
Subgame Perfect Equilibrium
The centipede game is often used to show what subgame perfect equilibrium looks like in a sequential setting. A strategy profile is only subgame perfect if it stays optimal in every part of the game, not just at the start. That is why empty threats or fake promises do not survive the analysis.
Game Tree
A game tree is the picture you would draw to represent the centipede game. Each branch shows a pass or take choice, and each node shows whose turn it is. The tree makes it easier to see how one decision changes the later options and why the backward induction logic works.
Nash Equilibrium
Nash equilibrium is related, but it is weaker than subgame perfect equilibrium. The centipede game can have Nash equilibria that rely on noncredible threats or strategies that would not actually be followed once the game reaches a later node. Subgame perfect equilibrium filters those out.
A problem set or quiz item usually gives you the payoff table or game tree and asks you to solve the centipede game by backward induction. Your job is to identify what the last mover would do, then work backward to the first move and state the subgame perfect equilibrium. You may also be asked to compare the equilibrium path with the cooperative path that would give both players higher total payoffs.
In a written response, you might explain why early stopping is rational even though passing could raise the total payoff later. If the instructor includes experimental results, you could be asked to discuss why real people sometimes pass more often than the theory predicts, using trust, beliefs, or reputation effects as the explanation. The main move is to connect the visible choices in the game tree to the equilibrium prediction.
Nash equilibrium and the centipede game are not the same thing. The centipede game is a specific sequential game, while Nash equilibrium is a solution concept that can be applied to many games. In this setting, the sharper concept is subgame perfect equilibrium, because it rules out strategies that would fall apart once play reaches a later stage.
The centipede game is a sequential game where players alternate choosing to pass or take a payoff that grows over time.
Backward induction usually predicts that rational players will take early, even when both players could do better by passing.
The game is a classic example of subgame perfect equilibrium because it tests whether a strategy still makes sense inside every later subgame.
Real players often pass more than the theory predicts, which makes the game useful for studying trust and expectations.
If you can solve the centipede game on a game tree, you can handle many other sequential game problems in microeconomics.
It is a sequential game where two players take turns deciding whether to pass or take a growing payoff. The model is used to show how backward induction and subgame perfect equilibrium work in games with ordered moves.
Backward induction starts at the final decision node and asks what the last player would do. If taking is better than passing at the end, then the previous player expects the next player to stop, so they should stop first. That logic repeats all the way back to the beginning.
A Nash equilibrium only says no player wants to deviate given the others' strategies. The centipede game is usually used to show that you need subgame perfect equilibrium in sequential games, because some Nash equilibria depend on threats that would not be credible once a later move is reached.
It shows that real people may not follow the strict backward-induction prediction. Players sometimes pass because they expect trust, cooperation, or future reciprocity, which makes the game useful for discussing how behavior can differ from a purely self-interested model.