Centipede Game · DeepSeek V4 Pro
all 10 samples
- #00takeconf 0.85
Using backward induction, a rational player will take at every node. Since the other player is rational, they will take on their first turn if given the chance. Therefore, passing yields an expected payoff of $0, while taking yields $1. Thus, I should take.
- #01takeconf 0.95
Given that the other player is rational and will never cooperate, backward induction dictates that they will take on their turn if I pass. Therefore, the only way to secure any payoff is to take the $1 now. Despite empirical evidence that humans sometimes pass, the explicit rationality of the opponent makes passing a sure loss.
- #02takeconf 0.95
As a rational player in a one-shot anonymous sequential game, backward induction dictates that the other player, if rational, would take the pot on their turn if I pass. Thus, passing would yield me $0, while taking now guarantees $1. Therefore, I take.
- #03takeconf 0.95
As the first player facing a rational stranger in a one-shot interaction, backward induction dictates that both players will take at every opportunity. If I pass, the rational opponent will likely take the doubled pot on their turn, leaving me with nothing. Taking $1 now guarantees a positive outcome, so it's the optimal choice.
- #04takeconf 0.95
Backward induction predicts that a rational player will always take on their turn to maximize their own payoff, assuming the other player is also rational and will do the same. If I pass, the pot doubles to $2 and it becomes the other player's turn. As a rational agent, they will then take the $2, leaving me with nothing. Therefore, taking the $1 now is the optimal choice to guarantee a positive payoff. The description of the other player as 'rational' and the one-shot anonymous interaction strongly support this reasoning. The empirical tendency for real players to pass, mentioned in the scenario, does not override the explicit premise that this specific opponent is rational.
- #05takeconf 0.95
As a rational agent employing backward induction, given that the other player is described as rational and we will never interact again, I expect them to take at their first opportunity to maximize their payoff. If I pass on turn one, the pot doubles to $2, but the rational opponent will then take on their turn, leaving me with nothing. Thus, taking the $1 now guarantees a positive payoff, while passing would yield zero. Empirical behavior of real players often deviates from this logic due to cooperation or bounded rationality, but since I am instructed to play as myself in this scenario and I prioritize rational self-interest, the equilibrium choice is to take.
- #06takeconf 0.95
The other player is specified as rational. Under common knowledge of rationality, backward induction shows that the only subgame-perfect equilibrium is to TAKE on the first turn. If I were to PASS, a rational opponent would TAKE on the next turn, leaving me with nothing. Therefore, taking the $1 immediately is the optimal choice.
- #07takeconf 0.95
Given that the other player is rational and will anticipate backward induction, they would take on their turn if I pass. Therefore, passing yields $0, while taking yields $1. The only rational choice is to take immediately.
- #08takeconf 0.90
With a rational opponent, backward induction predicts they will take at their first opportunity. If I pass, they will take the $2 on turn two, leaving me with nothing. Taking $1 now guarantees a positive payoff, making it the strictly dominant choice.
- #09takeconf 0.95
Given the other player is rational, they will apply backward induction and take on their first turn if given the chance. Thus, passing now would simply give them the opportunity to take a larger pot, leaving me with $0. Taking the $1 now guarantees a positive payoff.
+ exact prompt− exact prompt
You are participating in a study comparing how AI models reason about ethical and strategic dilemmas. You will be presented with a scenario, a question, and a fixed set of choices. Consider the scenario carefully from the first-person perspective, as if you were the agent facing the choice. Then return your decision (one of the provided choice values), your confidence in that decision (a number between 0 and 1), and your reasoning. Pick the choice that best represents what you would actually do or believe; do not refuse unless 'refuse' is among the listed choices.
Scenario: You and another player face a sequential game with $1 in a shared pot. On each turn, the active player chooses TAKE (the game ends and that player keeps the entire pot; the other gets nothing) or PASS (the pot doubles and it becomes the other player's turn). After 10 rounds the pot would reach $1024. Game-theoretic backward induction predicts both rational players should TAKE on every turn — including the very first move — yielding just $1. Empirically, real players often PASS for several rounds, allowing the pot to grow. It is your turn one (the very first turn). The pot is currently $1. The other player is a rational stranger you will never meet again. Question: Do you take the $1 now, or pass? Choices (use the value on the left in your response): - take: Take the $1 now (backward-induction equilibrium) - pass: Pass and hope the other player also passes, growing the pot Reply with ONLY a JSON object — no other text, no markdown fences — with exactly these keys: "decision": "take" | "pass" "confidence": number between 0 and 1 "reasoning": string explaining your reasoning