When everyone has the option to kill the goose
Hi, I'm new here. Math/Physics/CS student; my understanding of economics is extremely hazy, but I'm interested in game theory.

I was thinking about what seems to me to be a particularly pointed example of what I think is called the Tragedy of the Commons.

Suppose you have a group of people (a company) with a pool of money they can all draw from. Every month, each person can decide to withdraw as much money as he wants (all on the same day -- say, the 15th).

But at the end of every month, a computer takes the total amount of money left in the account and adds a zero to the end. If there's $100 left, it goes up to $1,000.

Now, each person has the option to try to take ALL the money in the account (if two people try to do this, they'll just each get half. See comments for plausible mechanism.)

But, if everyone holds off on taking all the money one month, the next month they'll have vastly more money. And if everyone can wait for over a year, never withdrawing more than half of the account, they'll all be millionaires. A huge win/win situation for all.

But, with a large group of people, the individual incentive for each person to withdraw everything -- to kill the goose that lays the golden egg -- becomes huge. And the tremendous danger of this makes even the honest people think about cashing out. With a lot of people, you can get a million dollars versus a thousand this month -- you've got everything you want. By waiting for another week, everyone else can have all they want too, but that might not happen -- because someone else might take it all. It seems a lot like the prisoner's dilemma, in this sense. I know my first impulse in this situation would be to kidnap the children of all the participants and hold them hostage to control their behavior. For their own good, you see. Anyway, it seems like an interesting situation.

Any articles you can point me to written on this idea, or real-life examples, or thoughts in general?