What is a cheap technology to allow multiple devices to know each other when close in proximity?
A cheap old fashioned way is by audio. Simply have a small speaker and microphone on each device. Different frequency for each ID, or use one frequency and have each device transmit an ID continuously after a pause of random length. Tiny millisecond long clicks at >20kHz will easily be enough and won't be audiable to humans.

You could even use volume to guestimate distance between them.