You may have been the other computer (it happens sometimes). But to your question, open airport utility and clock on the router, it should show all connected clients.
What router are you using? A lot of routers have logs you can look at. Plus since Dashboard is still in 10.9 then get the Dashboard program WhoisConeected.
Also consider getting the shareware program Little Snitch. Then you could monitor every packet going out of your Mac.
One way that you can get the "Another device on the network is using your computer's IP address" message is the following scenario that has happened to me:
1) you have multiple devices connected to your router and your router reboots while one of those devices is in sleep mode;
2) you then start your computer and the router assigns it an IP address; the IP address may be the same as the sleeping device because the router lost that information when it rebooted;
3) when the sleeping device is then used it triggers the duplicate IP address message.