Inside the mind of a fair player cooperating

LessWrong reports a fresh perspective on how proof‑based agents can reliably cooperate in a prisoner's dilemma. The post contrasts an older fairness rule—cooperating only when you can prove the opponent will cooperate—with a new definition that treats betrayal as a provable defect against a cooperating opponent, showing that fair agents never betray and therefore choose to cooperate. By invoking Löb's theorem, a well‑known result in mathematical logic about self‑referential provability, the author demonstrates that each player can find a proof of the other's cooperation, guaranteeing a cooperative outcome. The conclusion suggests this clearer fairness definition could make proof‑based decision theory feel less like magic and more tractable.

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