[mathking]

The colluded shutout agreement runs some significant risk for the "winning" alliance in that if they get any penalties, they will actually come out behind the "losing" alliance in seeding points for that round. You could argue that if they two alliances cooperate they might still score more points than they would have scored if the match had been played with both alliances trying to get the most points. But I suspect that a lot of teams will be unwilling to risk what they might view as an unfair result.

One thing I think is clear is that in most unbalanced matches without any collusion, there will be a point at which the sides start trying to score for each other. If there are 30 seconds left and you are up 12-1, you have more incentive to put in balls for the opponents than for yourself. Furthermore, unless you have a reasonable chance to overtake the other side, you have no in-game incentive to try to hang from the bar if you are the losing side. All you will be doing is giving twice as many points as you earn to the winning alliance, while giving none to yourself.

Again I will say that this is a REALLY interesting game theory problem. I wish I were still teaching discrete math, because I would love to have a test question asking students to devise and justify a good strategy for the game.