A condition, not a universal theorem.
The model checks
R ≥ (1−δ)(T−q·s) + δ[qP+(1−q)R] for
infinite repeated play, stationary payoffs,
risk-neutral agents and credible grim-trigger
punishment. Public detection has a fixed probability
q and no false positives. A detected unilateral
deviation is slashed once and triggers punishment;
an undetected deviation returns to cooperation.
Enforcement and punishment credibility are
assumptions.
The original simulator’s
--delta remains an update rate. It does
not implement this discount factor.