# Game Theory Problem

• Jan 6th 2008, 02:28 PM
LibertyMan
Game Theory Problem
Hello everyone. I had a couple of interviews to read PPE at the University of Oxford last month, one of which involved talking about a problem that you had been given a quarter of an hour to think about. I got offered a place on the course, so I'm guessing that I got somewhere towards solving it, but I was wondering if somebody a bit more knowledgeable on game theory than me could share their insights:

"Imagine you are placed in the following scenario. You are alone in a room which contains a pound coin, a pay-phone and a scrap of paper with a phone number on it. There are one million identical rooms in the building, each containing a single person. Every person can choose to do one of the following:

A. Use the coin to call the number, if somebody older than them also calls then they win one million pounds (the younger caller wins the million). If nobody older than them calls, then they leave with nothing.

B. You can take the £1 and leave, never to return.

What would you do?"

Some questions that came up:
What if you got to play this more than once?

What if everybody playing knew everybody else's age?

I'm fairly certain that I'm right when I say that the eldest person would know he couldn't win, and therefore would not call. The next eldest person would realise this, so he wouldn't call either, and so on until everybody has take the coin, and left.

Does the last question change the answer to the original problem?
• Jan 7th 2008, 12:12 AM
CaptainBlack
Quote:

Originally Posted by LibertyMan
Hello everyone. I had a couple of interviews to read PPE at the University of Oxford last month, one of which involved talking about a problem that you had been given a quarter of an hour to think about. I got offered a place on the course, so I'm guessing that I got somewhere towards solving it, but I was wondering if somebody a bit more knowledgeable on game theory than me could share their insights:

"Imagine you are placed in the following scenario. You are alone in a room which contains a pound coin, a pay-phone and a scrap of paper with a phone number on it. There are one million identical rooms in the building, each containing a single person. Every person can choose to do one of the following:

A. Use the coin to call the number, if somebody older than them also calls then they win one million pounds (the younger caller wins the million). If nobody older than them calls, then they leave with nothing.

B. You can take the £1 and leave, never to return.

What would you do?"

Some questions that came up:
What if you got to play this more than once?

What if everybody playing knew everybody else's age?

I'm fairly certain that I'm right when I say that the eldest person would know he couldn't win, and therefore would not call. The next eldest person would realise this, so he wouldn't call either, and so on until everybody has take the coin, and left.

Does the last question change the answer to the original problem?

The purpose of the question is to test your thinking so there is not a right or wrong answer.

Having said that I would claim that the simple game theory approach is
inappropriate (at least for me). A pound has negligable utility while a million
pounds has considerable utility (more than 1 million times that of 1 pound).
Also I would be happier that someone has the million than that one one has it.

I would always phone, and I don't care that game theory tells me that I am
wrong.

(using the kind of logic that is indicated: if everyone knew everyone else's
age the youngest would phone, and no body else would, but the youngest
would know that so would not bother

The point about repeated play is that there is the possibility of passing
information between the players by the way people play so a colation may be
possible but I don't see how this can be made to work at present)

RonL
• Jan 7th 2008, 03:23 AM
Isomorphism
Quote:

Originally Posted by CaptainBlack
The purpose of the question is to test your thinking so there is not a right or wrong answer.

Having said that I would claim that the simple game theory approach is
inappropriate (at least for me). A pound has negligable utility while a million
pounds has considerable utility (more than 1 million times that of 1 pound).
Also I would be happier that someone has the million than that one one has it.

I would always phone, and I don't care that game theory tells me that I am
wrong.

(using the kind of logic that is indicated: if everyone knew everyone else's
age the youngest would phone, and no body else would, but the youngest
would know that so would not bother

The point about repeated play is that there is the possibility of passing
information between the players by the way people play so a colation may be
possible but I don't see how this can be made to work at present)

RonL

Incidentally this problem is similar to the hard riddle(in various forms), very popular as the "surprise quiz dilemma". Here is one such interpretations:

Quote:

The professor for class Logic 315 says on Friday: "We're going to have a surprise quiz next week, but I'm not telling you what day... if you can figure out what day it will be on, I'll cancel the quiz."

The students get together and decide that the quiz can't be on Friday, as if the quiz doesn't happen by Thursday, it'll be obvious the quiz is on Friday. Similarly, the quiz can't be on Thursday, because we know it won't be on Friday, and if the quiz doesn't happen by Wednesday, it'll be obvious it's on Thursday (because it can't be on Friday). Same thing for Wednesday, Tuesday and Monday. So it can't be on ANY day, so there's no quiz next week!"

They tell the professor, who smiles and says, "Well, nice to see you're thinking about it."

On Tuesday, the professor gives the quiz, totally unexpected!

What's the flaw in the students' thinking?