Contagious yawning, emotional contagion and empathy are characterized by the activation of similar neurophysiological states or responses in an observed individual and an observer. For example, it is hard to keep one's mouth closed when imagining someone yawning, or not feeling distressed while observing other individuals perceiving pain. The evolutionary origin of these widespread phenomena is unclear, since a direct benefit is not always apparent. We explore a game theoretical model for the evolution of mind-reading strategies, used to predict and respond to others' behavior. In particular we explore the evolutionary scenarios favoring simulative strategies, which recruit overlapping neural circuits when performing as well as when observing a specific behavior. We show that these mechanisms are advantageous in complex environments, by allowing an observer to use information about its own behavior to interpret that of others. However, without inhibition of the recruited neural circuits, the observer would perform the corresponding downstream action, rather than produce the appropriate social response. We identify evolutionary trade-offs that could hinder this inhibition, leading to emotional contagion as a by-product of mind-reading. The interaction of this model with kinship is complex. We show that empathy likely evolved in a scenario where kin- and other indirect benefits co-opt strategies originally evolved for mind-reading, and that this model explains observed patterns of emotional contagion with kin or group members.