The most popular, most famous, most mentioned exemplar in game theory, especially in the social sciences, is the ‘Prisoners’ Dilemma’ – which is actually a predicament, rather than a dilemma. Two men – all we know is their gender – charged with a joint violation of the law, are held separately by the police. Each is told that, if one confesses and the other does not, the former will be given a reward of one unit and the latter will be fined two units; if both confess, each will be fined one unit; if neither confesses, both will go free. Each of the two suffers less by confessing, but if they could reach a binding agreement they would clearly agree not to confess. As originally presented in an unpublished note by Albert Tucker and, usually, followed faithfully by game-theoretic analysts, all we know – as noted – is their gender. It usually follows, at least by implication, that both confess, contrary to their joint interest. I argue here, however, that we cannot conclude that the two are likely to confess. My argument will be simply that we do not know what they know and cannot predict what they will decide.