3-player push problem. Collusion?

[trojanrabbit]

Imagine this problem that isn't too far removed from realistic holdem problems. There are 3 players with $12 each. 2 players post blinds of $1/$2 and then each player must either push or fold. What is the optimum play for each player?

The 2-player version is fairly easy to solve, and is essentially the same strategy used when the button folds in the 3-player game. But I've heard that most (all?) 3-player poker games involve collusion in figuring out their optimum strategy. Is there any way that I can prove/disprove that it's the case for this game? I guess I can't intuitively see how collusion could work in this game if everyone is aware of everyone elses strategy. Anyone have any ideas on this?