We propose a simple mechanism that sustains full cooperation in one-shot social dilemmas among a finite number of self-interested agents. Players sequentially decide whether to contribute to a public good. They do not know their position in the sequence, but observe the actions of some predecessors. Since agents realize that their own action may be observed, they have an incentive to contribute in order to induce potential successors to also do so. Full contribution can then emerge in equilibrium. Our mechanism also leads to full cooperation in the prisoners' dilemma.