Two rivals each do better by BETRAYING — whatever the other does, defecting pays more. So both defect and both end up worse than if they’d cooperated. Rational self-interest drives them straight into the bad outcome. It is the cold heart of arms races, overfishing, and price wars. Slide the shadow of the future and watch when cooperation can survive.
The Prisoner’s Dilemma has payoffs T > R > P > S (Temptation, Reward, Punishment, Sucker): here T=5, R=3, P=1, S=0. DEFECT strictly dominates — against a cooperator 5>3, against a defector 1>0 — so the unique Nash equilibrium is mutual defection (1,1), even though mutual cooperation (3,3) Pareto-dominates it. Individually rational, collectively ruinous. ITERATED, though, a long shadow of the future (repeated play) can sustain cooperation via reciprocity. A fail-loud self-check throws unless defect dominates and (C,C) beats (D,D). ◆ real game theory, node-verified.
The canonical one-shot PD payoffs (the exact dominance and Pareto ranking); real dilemmas vary the numbers and add repetition, reputation and enforcement that rescue cooperation — the defection-dominates, everyone-worse core is exact.