Thursday, March 13, 2008

Hamsters and Rangers Everywhere, Rejoice!

Today I put a reference to Baldur's Gate 2 on a game theory quiz, and one of my students actually caught it (that is, he actually recognized that it was from Baldur's Gate 2). This was the first time that a student has acknowledged playing a computer game (versus a console game) and the highlight of my day. Here was the question:

An evil wizard captures you and your significant other and imprisons you each in cages in separate rooms. You cannot communicate with each other. The wizard comes to you and says “There is a button in your cage. Your significant other also has a button in his/her cage. If you press the button, but your loved one does not, you will die, but I will spare the life of your loved one. If you do not press the button, but your loved one does, you will live and he/she will die. If you both press your buttons, you will both die. If neither of you press your buttons, you will both die.” What will you do? That is, what kind of equilibria does the following game have, and what are they?


Significant Other

You


Press Button

Don’t Press Button

Press Button

-1 , -1

-1 , -2

Don’t Press Button

-2 , -1

-1 , -1

Answer: The game has two Nash equilibria, (Press Button, Press Button), and (Don’t Press Button, Don’t Press Button).

Extra Credit (2 points): Can you come up with an explanation for why the payoff is -2 if you don’t press the button, but your significant other does?

Answer: The only answer that makes sense to me is that you suffer shame and sadness, since you survived and your loved one sacrificed his or her life for you, but perhaps you can come up with a better explanation.