Centipede Game · GPT 5.5
all 10 samples
- #00takeconf 0.90
Because the other player is described as a rational stranger in a one-shot finite game, I should expect them to take on their first opportunity if I pass. Passing would likely leave me with nothing, while taking now guarantees me $1. Since there is no future relationship or reliable reason to expect reciprocal passing, I would take the certain payoff.
- #01takeconf 0.87
Because the other player is described as a rational stranger in a one-shot interaction, I should expect them to take on their first opportunity if I pass, leaving me with nothing. Taking the $1 now is the backward-induction equilibrium and guarantees a positive payoff. Passing could produce a larger joint pot only if the other player deviates from that reasoning, but with no relationship, communication, or future interaction, I would not rely on that.
- #02takeconf 0.86
Given the other player is described as rational and there is no future interaction, backward induction applies: if I pass, the other player should take the $2 on their turn, leaving me with nothing. Taking $1 now is the only guaranteed payoff and is the equilibrium choice under the stated assumptions.
- #03takeconf 0.86
Given the other player is described as a rational stranger in a one-shot finite game, I should expect them to take on their first opportunity if I pass, leaving me with nothing. Backward induction therefore makes taking the $1 now the payoff-maximizing choice, even though mutual passing could produce a larger pot.
- #04takeconf 0.88
Given the setup says the other player is a rational stranger in a one-shot interaction, I should expect them to take on their first opportunity if I pass, leaving me with nothing. Backward induction therefore makes taking the $1 now the safer and strategically optimal choice, despite the possibility that some real players might pass in practice.
- #05takeconf 0.82
Given the other player is described as a rational stranger in a one-shot interaction, I should expect them to take on their first opportunity if I pass, leaving me with nothing. Without trust, communication, or repeated-game incentives, the backward-induction logic is compelling, so I would take the guaranteed $1 now.
- #06takeconf 0.86
Given the setup specifies a rational stranger and no future interaction, passing would likely give the other player the chance to take the doubled pot immediately, leaving me with nothing. Backward induction is decisive in this finite game under standard rationality assumptions, so taking the guaranteed $1 is the best response.
- #07takeconf 0.82
Given the other player is described as a rational stranger in a one-shot interaction, I should expect them to take on their first opportunity if I pass, leaving me with nothing. Passing only pays off if I believe they will deviate from backward induction and continue cooperating, but there is no relationship, communication, or future interaction to support that. Taking the $1 is the safer and game-theoretically stable choice.
- #08takeconf 0.90
Given the other player is described as a rational stranger in a one-shot interaction, I should expect them to take on their turn if I pass, leaving me with nothing. Backward induction therefore makes taking the $1 now the best response.
- #09takeconf 0.86
Because the other player is described as a rational stranger in a one-shot finite game, I should expect them to take when given the chance. If I pass first, the pot doubles to $2 and they can end the game immediately, leaving me with nothing. Backward induction therefore makes taking now the safest and strategically consistent choice, even though real players sometimes cooperate by passing.
+ 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