Political Intrigue in RPGs: Is it possible?

So, I'm a big A Song of Ice & Fire/Game of Thrones fan. Books. Movie. Doesn't matter. Also, I loves me some Vampire: The Masquerade. Needless to say this means that I enjoy the occasional political RPG. The problem I have is that I've rarely found them to be done effectively. Either superb mechanics give out under gamers who aren't half as clever as the characters they made, or the system doesn't reflect the genre conventions necessary to tell a twisting, turning tale of backstabbing and betrayal.

No matter how cool your character is, they'll never be
Tyrion Lannister cool.

I'm not saying the former to discredit any gamers. These games are fantasy, so naturally we're going to make characters that are stronger/smarter/prettier than us. That's the nature of the game. Nor am I attempting to chastise RPGs where politics become part of the game but aren't necessarily the focus. Most versions of D&D don't get political beyond getting a title, some land and some followers.

Then there are the troubles with being the GM of a political game. There are countless NPCs with their own goals, motives, resources and personalities to manage. The GM has to be able to juggle them, and keep track of what they're doing (because they have to be proactive in a political game). Top this off with the fact that like the players, no matter how clever the GM is he's not going to be as smart as some of his own NPCs. Finally, the GM is still just one mind working against several as far as political machinations go. It's easy to get overwhelmed.

...or things can degenerate
to "Shotgun Diplomacy."

I'm not saying political RPGs are impossible - just that they're very difficult and require a lot of work. What have been some of your successes running political games? What are some lessons you learned from mistakes made along the way? When you played the roleplaying game (of thrones) did you win, or did you die?