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And then one person says that they chose 6 points and haven't won it via lottery. The other students can't retaliate because the only way to get back at her would be to take away points from the entire group

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They can retaliate, there's simply a cost associated. That's one of the reasons this is a poor exercise: In iterative games it's often worth making sure people know that certain kinds of behaviour don't work - even where you have to harm yourself in order to do so. Otherwise you'll always be held hostage by those willing to move the costs closest in time.

I suspect this is why hatred and resentment are part of our make up.

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