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I cannot attack someone. The game says I have a shared connection with him, but I don't.

Shared connections block all actions that would otherwise be against the game rules while sharing the same internet connection. Interacting with a player that already had actions directed at him by someone you share your connection with would be against these rules, so the system blocks it. 

It doesn't necessarily mean you have a shared connection with this other player, it means that someone you share your internet connection with already had an interaction with him in the last 48 hours, so you must wait a bit before you can take your turn.