In one embodiment, a method comprises: determining, by a constrained network device in a low power and lossy network (LLN), a self-estimated density value of neighboring LLN devices based on wirelessly receiving an identified number of beacon message transmissions within an identified time interval from neighboring transmitting LLN devices in the LLN; setting, by the constrained network device, a first wireless transmit power value based on the self-estimated density value; and transmitting a beacon message at the first wireless transmit power value, the beacon message specifying the self-estimated density value, a corresponding trust metric for the self-estimated density value, and the first wireless transmit power value used by the constrained network device for transmitting the beacon message.