One might be able to do this with peer to peer networking through WebRTC. You still need a way to send each phone an SDP offer/answer but maybe this could be done with QR codes.
Might be a fun demonstration project for persons or orgs wanting to show off distributed consistency protocols. You might even add some blockchain to the mix if you have a thing for stale buzzwords. For a company with a product in the distributed consistency field, it could make a nice trade show booth giveaway: "this is actually our product, and you can even challenge each other on the plane back home, that's how special it is"