Building on classic game theory, psychologists have explored the effects of social preferences and expectations on strategic behaviour. Ordinary social perceivers are sensitive to additional contextual factors not addressed by game theory and its recent psychological extensions. We review the results of a research programme exploring how observers judge “players” (i.e., individuals making strategic decisions in social dilemmas) on the dimensions of competence and morality. We explore social perception in several well-known dilemmas, including the prisoner’s dilemma, the volunteer’s dilemma, and the trust dilemma. We also introduce a novel self-presentational dilemma. In research conducted over a decade and a half, we have found that judgements of competence are sensitive to both players’ choices and the dilemma’s (expected and actual) outcomes. In contrast, judgements of morality respond strongly to players’ behaviour and little else. We discuss how these social-perceptual patterns might affect expectations, preferences, and strategic choices.