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We present a successful design approach for social robotics based on a computational cognitive architecture and mental simulation. We discuss an approach to a Theory of Mind known as a “like-me” simulation in which the agent uses its own knowledge and capabilities as a model of another agent to predict that agent’s actions. We present three examples of a “like-me” mental simulation in a social context implemented in the embodied version of the Adaptive Control of Thought-Rational (ACT-R) cognitive architecture, ACT-R/E (for ACT-R Embodied). Our examples show the efficacy of a simulation approach in modeling perspective taking (identifying another’s left or right hand), teamwork (simulating a teammate for better team performance), and dominant-submissive social behavior (primate social experiments). We conclude with a discussion of the cognitive plausibility of this approach and our conclusions.