Friday, November 10, 2006

Random Games

Most students of Political Science have heard of the Game Theory. Few have seen it in action. Over the weekend, I had the joy of doing just that.

My Gentleman and I went to Phoenix for the first weekend in November and had the (mis)fortune of staying at the same hotel as a visiting high school band. Visions of giggly, screaming, hormone-driven teenagers put a bit of a damper on our romantic inclinations. Surprisingly enough, the kids were rather quiet once 10 o’clock rolled around.

Sure, prior to that we could hear them banging around and chatting as they gossiped up and down the hallway. But the few chaperones shepherded the students into their rooms and there those kids stayed.

I was amazed at how the limited number of adults – probably in great need of sleep after a day of dealing with a marching band full of teenagers – managed to keep the kids in their rooms and out of trouble. Around 11pm, my Gentleman had gone out to get some ice for his Coke and came back with the answer.

The solution to keeping all the students in their rooms was to put a piece of cellophane tape over the gap above the doorknob on each door. It if was broken when the chaperones went to knock on the door to wake the occupants up in the morning, then all the students within that room were in trouble.

It had me thinking about Game Theory.

Given that each room has a phone, and thus the occupants could call each other and arrange a “jail break”, it would be possible to communicate and plan. All students who wished to break out and sneak from room to room could conceivably do so. The problem would be that only the last student to return to his/her room would have the telltale broken tape, as that student would be able to replace the tape to everyone else’s door, thus the only ones who would be punished would be the occupants of that last room.

Given this scenario, what would you do?
Situation A: your friend calls, asking that you come out, promising that you can return to your room before the friend, the tape on your door would be replaced and appear to be unbroken. However, you run the risk that your friend might not honor the promise.
Situation B: your friend calls and asks that you let the friend out so the tape on that door would be unbroken, while the one on yours would be, but if things get interesting for the friend, you can go back to your room and the tape on your door will be replaced.
Situation C: it’s the friend of your roommate who calls to suggest either Situation A or B to the roommate, but you don’t leave the room and will get in trouble along with the roommate if the tape on the door to your room is broken.
Situation D: cooperate with the chaperones and tell anyone who calls to bugger off.

Hmmm. Not quite Prisoner’s Dilemma nor Stag Hunt, that’s more like Chicken or Volunteer really. Perhaps we should call this one Big Band Theory

All I know is that the students seemed to pick D, because we had a lovely, restful night with nary a giggle to be heard after 10pm.

1 comment:

Anonymous said...

A note from "The Gentleman" in question: you forgot option "E" Mutually Assured Distruction. Students in rooms 1, 2 and 7 sneak out, and while out, cut the tape on all other doors, thus making it impossible to tell who really got out, thus diffusing blame and rendering disipline impractical. I had a horse once who practiced this strategy. She'd pick the lock on her stall, get loose, let everybody *else* loose, and then go break into the room where we kept the grain and molasses. (Yummy treats to a horse.) She figured since everybody else was loose, we couldn't pin it on her. She forgot that she lacked both thumbs and a mirror. She was the only horse with sticky grain stuck to her face, thus making the assignment of guilt simple. Nice try though.