Communication between iOS app installed on different devices on the same LAN

Socket.IO is nice because it is fairly simple to implement but it has the downside of requiring a central server. If you wanted to avoid that, you could use the Multipeer Connectivity framework that was introduced in iOS 7.

It will let you create one-to-one communication channels between devices on either the same WiFi network or Bluetooth. Once the channel is created, you can send whole NSData objects (or create streams but it doesn't seem relevant to your use case).

A good read : http://nshipster.com/multipeer-connectivity/

The WiTap sample from Apple demonstrates peer-to-peer networking over Wi-Fi and Bluetooth. Using Bonjour, the application both advertises itself on the local network and displays a list of other instances on the network. Supports infrastructure networks, peer-to-peer Bluetooth, and peer-to-peer Wi-Fi (on compatible hardware).

I have personally tested it and it works fine and well documented.