Two people in a greed therapy group are playing a game. There is a pot of 6 dollars and each person, while isolated, is asked the question "Do you want to be greedy and take all of it?" The money goes to the person who is greedy and if they answer the same they share it. To punish their greed, a player must pay 1 dollar of what he won if he were greedy and an extra dollar if both players were greedy.

__
You \ Other | Not Greedy | Greedy |
Not Greedy | 3\3 | 0\5 |
Greedy | 5\0 | 1\1 |__

A) Which option should you choose the first time you play?

B) If you continue playing an unknown finite number of games, what strategy should you use to maximize the amount of money you can win? (Assume that your opponent doesn't necessarily use the same strategy as you.)

Note: Both players are trying to get as much money as possible, and neither needs to get a certain amount of money at all costs.

If both players want to maximize their winnings I would think they'd cooperate each turn.

If both were to take a typical PD strategy of doing whatever their opponent did last time, they may end up alternating (5/0) and (0/5) rounds. Unfortunately, a dollar is lost each time this is done. So after 2 rounds of alternating like this, each has 5 dollars. If they had cooperated, they would instead each have 6 dollars.

I'm a nice guy, so I'd start by cooperating. :)