Collusion Possibilities in Sinquefield Cup:

Going in to the last round we have:

Carlsen: 3.5, Naka: 3, Levon 2.5, Gata 1

Prize Structure  ($k) is: 70/50/30/20

Here is my analysis, assuming full player collusion:

Match 1: Gata-Naka

If Gata wins, he is still getting last place, whereas a win for Naka is of huge benefit. Optimal strategy with collusion is a Gata loss (finishing with 1 point), and a Naka win (finishing with 4).

Match 2: Magnus-Levon

Both these players realize that the dominating strategy from other match will be a Naka win. Levon reasons that if he draws or loses, he will be getting third place regardless, so no reason to fight for a draw. If he wins, he splits 2nd and 3rd with Carlsen (40 each), whereas if he loses Magnus gets clear 1st (70) and he gets clear 3rd (30). So clearly the optimal strategy with collusion is Carlsen wins, as more money can be earned jointly by this arrangement. 

So my questions are:

1) Is there any evidence that top players actually do collude in tournaments like this? Even not direct evidence but statistical evidence ...i.e.: last place player loses far more often then his rating normally would indicate?

2) Are there any other tournament formats that avoid such collusion possibilities? Even without any collusion, it is uninteresting from a spectatot's perspective that Gata is going into the last round with absolutely nothing to gain financially.

I highly doubt Gata will just tank a game with as badly as he's played.. if anything it would be the opposite.. he'll fight as hard as possible to salvage at least a less embarrasing score.