In social dilemmas, negotiations, and other forms of strategic interaction, mind-reading—intuiting another party’s goals and intentions—has an important impact on an actor’s own behavior. In this paper, we present a model of how perceivers shift between social projection (using one’s own mental states to intuit a counterpart’s mental states) and stereotyping (using general assumptions about a group to intuit a counterpart’s mental states). Study 1 extends prior work on perceptual dilemmas in arms races, examining Americans’ perceptions of Chinese attitudes toward military escalation. Study 2 adapts a prisoner’s dilemma, pairing participants with outgroup targets. Study 3 employs an ultimatum game, asking male and female participants to make judgments about opposite sex partners. Study 4 manipulates perceived similarity as well as counterpart stereotype in a principal-agent context. Across the studies, we find evidence for main effects of both stereotyping and projection and support for our central prediction: heightened levels of perceived similarity are associated with increased projection and reduced stereotyping.