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Toward enabling next-generation robots capable of socially intelligent interaction with humans, we present a computational model of interactions in a social environment of multiple agents and multiple groups. The Multiagent Group Perception and Interaction (MGpi) network is a deep neural network that predicts the appropriate social action to execute in a group conversation (e.g., speak, listen, respond, leave), taking into account neighbors' observable features (e.g., location of people, gaze orientation, distraction, etc.). A central component of MGpi is the Kinesic-Proxemic-Message (KPM) gate, that performs social signal gating to extract important information from a group conversation. In particular, KPM gate filters incoming social cues from nearby agents by observing their body gestures (kinesics) and spatial behavior (proxemics). The MGpi network and its KPM gate are learned via imitation learning, using demonstrations from our designed social interaction simulator. Further, we demonstrate the efficacy of the KPM gate as a social attention mechanism, achieving state-of-the-art performance on the task of group identification without using explicit group annotations, layout assumptions, or manually chosen parameters.