A group of students at Virginia Polytechnic Institute and State University have done a game theory project looking at the Parent's Dilemma in punishing children. Their analysis is available here. It is very insightful and interesting. I expect that got a high grade. What is good about it is that it does not presume that all parents are alike and demonstrates that some parents will have to favour different strategies depending on how much they hate (or I guess like me, enjoy) implementing punishments.
