The Prisoner's Dilemma (PD) exhibits a ‘tragedy’ in this sense: if the players are fully informed and rational, they are condemned to a jointly dispreferred outcome. In this essay I address the following question: What feature of the PD's payoff structure is necessary and sufficient to produce the tragedy? In answering it I use the notion of a “trembling-hand equilibrium”. In the final section I discuss an implication of my argument, an implication which bears on the persistence of the problem posed by the PD.