I think a good idea would be an interactive government thingy. One player would play as the Head of State, the others as members of the council and dictate how the country plays out. To make it more interesting, players could create their own characters and negotiate to others through letters. A good idea for this, I think, would be the French Revolution. The game would pass every week and the GM would make announcements (for example the formation of the National Assembley), among other things. I think that would have a lot of potential, think of all the other situations that could happen.