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Game Theory and Child-Rearing

A reader named Clark Case, who lives in Aurora, Ohio, and works as a product manager, writes in with a child-rearing observation. His kids are 7 and 4; his wife is a homemaker:

My wife came up with a punishment method for my kids that I thought that you (and perhaps your blog readers) would find interesting.
When the kids get to tussling and or screaming at each other in such a way that she is finding aggravating, she will send them to their respective rooms with the stipulation that they can come out when they both agree to apologize to each other.
Game theory, I suppose, would argue that they should immediately apologize to one another to minimize the period of detention. What seems to happen, though is that one will think that the other deserves some extended detention and will give up freedom himself in order to see that the other gets it.

Am interested to hear other game-theoretic attempts at child-rearing …