Inviting Friends in Magic 2012 for PC

I'm playing Magic: The Gathering - Duels of the Planeswalkers 2012 on PC via Steam, and I'm having a hard time connecting to friends. Whenever I create a new game, set a player slot to Private and click Invite, nothing happens. According to Gamespot, clicking Invite should bring up a Steam UI to let me select a friend. This is not the case, and I have to instead create a public game and hope my friend sees me and joins.

The game is running in "windowed" mode (fullscreen is turned off), and it doesn't seem to matter whether friends are online or playing the game - it still doesn't work. Everything else in the game works, including public online play.

Does anyone have a fix for this?

The invites in MtG:DotP don't always pop up for your friends like they're supposed to. However, your friends can still join your game: In the steam friend's list, they need to click the arrow next to your name, then click "join game." They can bring up the friend's list ingame by hitting shift + tab, or simply by minimizing the game (alt + tab) and opening it from Steam.

You can do the same thing to manually invite friends using your friend's list.

Note that joining and inviting to games both work for most multiplayer Steam games, not just Magic the Gathering.