The Office Pt. 2: Games within a Game and Buttlicker Challenges

The guys take a lot of joy in analyzing one of the funniest scenes in all of the Office, Jim's portrayal of the crusty customer, William M. Buttlicker (Season 5, Ep 7).  While this one is super lighthearted, there's still much to learn in our series about Game Theory.  How do you interact with a game within a game?  What do you do when one of the other players are having a bad day (or are just petty)? And what types of game do we benefit most from making unlikely alliances?