Analogous to “doctor shopping,” children practice parent shopping. My son comes to me and asks if he can play his computer game. When I say no, he goes and asks his mother. That is, assuming he hasn’t already asked her. After all how can I know that I’m not his second chance?
Indeed, if she is in another room and I have to make an immediate decision I should assume a certain positive probability that he has already approached her and she said no. Assuming that my wife had good reason to say no that inference alone gives me a stronger reason to say no than I already had. How much stronger?
If its an activity where he has learned from past experience that I am less willing to agree to, then for sure he asked his mother first and she said no. It’s no wonder I am the tough guy when it comes to those activities.
If its an activity where I am more lenient he’s going to come to me first for sure. But his strategic behavior still influences my answer. I know that if I say no, he’s going to her next and she’s going to reason exactly as in the previous paragraph. So she’s going to be tougher. Now sometimes I say no because I am really close to being on the fence and it makes sense to defer the decision to his Mother. Saying no effectively defers that decision because I know he’s going to ask her next. But now that his Mother is tougher than she would be in the first-best world, I must become a bit more lenient in these marginal cases.
(Addendum: If you want to know how to combat these ploys, go ask Josh Gans.)