Shake n Stomp

If you don't know the song I'm not surprised. A lot of my music tastes are fairly obscure, in this case 60s garage rock.

The purpose of this post is to examine why women appear so stubborn and irrational. Why they are infact rational, and why as a guy it's probably best just to let them get their way.

Assume that a boy and girl are in a relationship. The girl would like to go out to dinner. However she expects the boy to pay (which he would prefer not to).

To form a model I make the assumptions that dinner for the girl is worth +2 points, and for the boy -1 (because he doesn't want to go). Sex for the girl is worth +2 points and for the boy +3. These numbers are somewhat arbitrary but they can be adjusted within reason and the results are the same.

In my model I give each player two options, the boy can take her to dinner or not, the girl can have sex with the boy or not. I have tried to draw this in a table, I hope it works:

................................Girl
......................NO Sex.......Sex
..NO Dinner....0,0............3,2
..Boy
....Dinner........-1,2............2,4

The first number is the boys utility the second the girls.

From this assuming rational self-interest the Nash Equilibrium is Sex and No Dinner.

To elaborate, the girl would be rational to have sex even if she doesn't get to go to dinner because she gains some utility whereas otherwise she would gain none.

However, this is not what would happen. Because girls are stubborn! And boys know it. In actual fact the girl will only have sex if she gets to go to dinner even if this means she is not maximising her utility.

Because all guys know this then the options become.

No dinner = 0
Dinner = 2

Why is it that game theory apprently fails?

Because a more in depth understanding of game theory tells us that over multiple games things change. Dinner and sex can become a Nash equilibrium if the game is repeated. Infact I have reason to believe it is the most likely outcome based on pure mathematics. Firstly it has the highest total social outcome of 6, but I think more importantly is the concept of punishment. If the girl refuses sex because she does not get dinner her utility is 0. But her loss of utility is only 2. Her potential gain is +2. Therefore if she gets dinner next time the game is played she has already broken even, and assuming she gets even 2 dinners out of this there is a net gain. For the guy the punishment incurs a loss of 3 utility points. His possible gain by not buying dinner is only 1. The punishment is not only harder on him, his potential gain from being stubborn is less. In a stand off say he refuses her dinner twice he would need to have sex without paying for dinner 5 times to benefit! The girl could refuse sex twice and only need 3 dinners to win.

If the game theory is too much for you just take away this moral. Buy your girlfriend dinner, it is in your best interests.