Use of relative time of receipt of voice command as basis to control response to voice command

A system comprising multiple devices each having one or more respective microphones configured to receive audio, wherein the multiple devices are cooperatively configured to facilitate controlling which of the multiple devices will respond to a voice-command utterance, including:

• each given device of the multiple devices being configured to receive the voice-command utterance through the device's one or more microphones and to determine a respective time of receipt of the voice-command utterance by the given device,
• the multiple devices being configured to exchange with each other their determined respective times of receipt of the voice-command utterance, and
• each given device of the multiple devices being configured (a) to determine, based on the exchanging, whether any other device of the multiple devices received the voice-command utterance earlier than the given device and (b) to control whether the given device will trigger action in response to the voice-command utterance, wherein the controlling includes (i) if the given device determines based on the exchanging that no other device of the multiple devices received the voice-command utterance earlier than the given device, then the given device triggering action in response to the voice-command utterance, and (ii) if the given device determines based on the exchanging that any other device of the multiple devices received the voice-command utterance earlier than the given device, then the given device forgoing triggering of action in response to the voice-command utterance.