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.
The first option should be to be not greedy. Hopefully the other person picks similarly. If yes, repeat for the rest of eternity, until the other person becomes greedy or until eternity is reached, whichever is sooner. If not, in the next round instantly be greedy, and be greedy for the rest of eternity.

Posted by Jack Lim
on 20060302 08:08:36 