Battle of the sexes: Threats get results

The basic problem

Barack and Michelle trying to see the same movie at the cinema was the subject of a previous post. It was an example of a Battle of the Sexes game where Barack would rather see Horrible Bosses, and Michelle would rather see Bridesmaids. Whatever happens they would rather be together than watch different films. It is a co-ordination problem.

An extra twist

We will now make it a bit more interesting to see what happens.

Michelle’s last words to Barack that morning were:

“You know I love popcorn but I’m not going to have any tonight”

What difference could that possibly make?

When Barack arrives at the cinema Michelle has already gone into a movie, he has to try to go into the same one as her but he doesn’t know which one she has chosen. He knows that she has threatened to not have any popcorn. He then thinks that if she isn’t going to have her favorite snack then she will definitely want to see her preferred movie.

He knows this because not having popcorn and watching Barack’s favorite film, either with or without him, is worse than having popcorn and watching a film on her own. The only way she can be better off not having popcorn if to go to her favorite film.

Knowing this Barack chooses Bridesmaids.

Victory for Michelle

When he sits down next to Michelle she offers him some of her popcorn! Just making the threat meant that it was Barack’s best strategy to see her preferred movie, knowing that the threat would have led him to this conclusion she was free to buy the popcorn anyway. She didn’t need to follow through on the threat.

It is important to note that Michelle makes a threat to make her own position worse, she does not make a threat against Barack.

Today’s takeaway: Threats to make your own situation worse can change the outcome of a game, even if you don’t follow through with the threat.

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