I have been playing the card game Hanabi one hell of a lot recently, and I strongly recommend it to the LW community.

Hanabi is an abstract, cooperative game with limited information. And it's practically a tutorial in rational thinking in a group. Extrapolating unstated facts from other players' belief states is essential: "X did something that doesn't make sense given what I know; what is it that X knows but I don't, under which that action makes sense?" So, for that matter, is a consequentialist view of communication: "If I tell X the fact P, what will they do? Not what will they believe or know, but what actions should I expect they will take?"

Two people I've played with have told me that the game has positively affected their understanding of communication.