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Imitation is a very complicated function which requires a body mapping (a mapping from observed body motions to motor commands) that can discriminate between self motions and those of others. The developmental mechanism of this sophisticated capability, and the order in which the required abilities arise, is poorly understood. In this paper, we present a mechanism for the development of imitation through a simulation of infant-caregiver interaction. A model was created to acquire a body mapping, which is necessary for successful mutual imitation in infant-caregiver interaction, while discriminating self-motion from the motion of the other. The ability to predict motions and the time delay between performing a motion and observing any correlated motion provides clues to assist the development of the body mapping. The simulation results show that the development of imitation capabilities depends on a predictability preference (a function of how an agent feels regarding its options of “what to imitate,” given its ability to predict motions). In addition, the simulated infants in our system are able to develop the components of a healthy body mapping in order, that is, relating self motion first, followed by an understanding of others' motions. This order of development emerges spontaneously without the need for any explicit mechanism or any partitioning of the interaction. These results suggest that this predictability preference is an important factor in infant development.