Multiplayer
From The Blockheads Wiki
2 player mode lets you play "The Blockheads" with a friend via Apple's "Game Center."
Each time you play in a game world you can choose whether to play by yourself or invite a friend.
Although the game offers "Auto-match" in the Multiplayer Game screen, majicDave has stated:
Due to limitations in the way Game Center works I wasn't able to implement auto matching for multiplayer. I also couldn't disable the auto matching user interface. It's misleading I know and I hope to fix it somehow. But for now, the only way to play multiplayer is to invite a friend.[1]