The biggest issue is to know the ip address of the other devices. And even if you know them: via www they are not addressable (the main reason for a server) via 3/4G. In a local WiFi environment maybe (opening ports) but you don't know the ip address, too. You could then think about using email to exchange the data but this is slow and not meant for huge traffic.
So you need a server. If the main reason is NOT "cost"

but - let's say - privacy: think about encryption (RSA + AES).