I have been thinking that in most of the games there are plenty of people who are happy with second or third place and don't fight any longer to reach first place.
So what if we have a game mode which:

- can be ranked or not
- only the first will get a gold medal, the rest will not get anything
- if ranked only the first one will get an increase in rank, the rest will all decrease in rank (based on their position)
- in order to make sure that people don't team up in multiple games and let eachother win, the decrease in rank for second place and below should be enough so that, if you get second place in one game, you will need at least 2 wins to get back to your original rank

I believe this would make the game a little more cutthroat, forcing you to turn agains your allies.

I think this would mainly kill what Subterfuge is about. Only fighting for first place and being expected to be betrayed anytime if you seem like you are first would drive people paranoid in the course of a week. And about ''2 wins equal 1 loss'', that's the most harsh thing I have ever heard and lead to people never playing this mode.

I understand your point of view, then how about having a separate ranking system for this type of game mode. In my opinion it would be attractive to overachievers or people who like a chalange.
I'm not sure about making people paranoid, just more aware and they will have a certainty that it will be coming. It will not be something out of the blue or consider it a backstab.

Ranking systems like this would not work.....not because of the fact that no-one would play it, but the actual rating system just isn't supposed to work like that mathematically.
The average rating of all players in any rating system is supposed to stay at the entry rating (unless other factors are applied) If we make it so harsh that 2 wins = -(1 second place), then at least 14 wins = -(2-10th place added together)...this would just collapse the whole system. Ratings would get lower and lower and eventually reach 0...