## Wednesday, June 18, 2008

### A Little Game Theory

This is an optimization problem common to game theory. You want to get the most out of your situation, so it's not enough just to say I'd make the call or I'd take the buck. You have to explain why you would want to do so.

You are alone in a room which contains a one dollar 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 dollars (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 do you do?

I don't know if there's a right answer to this question. At least, I don't know what it is.

1. I would do choice a. Beacause um majority of them should be adults older than a teen tween or kid. So yeah I choose a.

2. It all depends on how old you are. If you are. Id say 18 would be the youngest age possible. closer you are to that age, the better chance I think you would have at getting a million.

If you are in your 80's or 90s... your possibly going to be older.

3. My Sister-In-Law Wendy said "The OLDER AND WISER ones took the silver dollar and left, because you can’t put a silver dollar in a pay phone?"

I said "I would definitely lose the dollar on a chance. What is a dollar anymore? Besides most of us lose more weekly on a chance...the lottery!"

4. I would take the dollar and leave. Yes, I’d leave with something cuz, If all the rooms are identical then everyone would be the same age. Nobody older would be there

I’d take the buck and go buy a lottery ticket

5. I believe there is the right answer and that is A.
Let's imagine that we run this situation say 1000 (or 100 000) times. I think there will be AT LEAST one time when somebody older than you phones. As a result, you win MUCH more money than you lost.
Run it infinite times and infinite amount of money choosing A option will be more than infinite amount of money as a result of B.

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