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.
(In reply to
Best way by Jack Lim)
Never thought I'd reply to myself, but I realised this may be necessary after viewing the answers of others.
Psychology 101 time.
If you were playing the game and the other person chose greedy immediately, while you chose not greedy, what would you do the next round?
You WILL be greedy the next round correct? If you do not he is liable to be greedy again and take $5 again. If you are greedy and he is not, you take $5. If you are not greedy and he is not, you get $3. If both sides are greedy, you get $1 each. Logically speaking, out of concern for your own welfare, you will be greedy, as no matter what he chooses, you will be able to get more. However, after you are greedy this time, the same thought process will go through the other player's mind. Therefore he WILL be greedy in the 3rd round, and as you know that you will be greedy in the 3rd round as well to earn that $1. And this stalemate will continue for the rest of eternity, hence the need to consistently choose to be greedy for the rest of the whole game.
Never choose to be greedy the first round as that results in an immediate stalemate with $1 each per round. Trust that the other person has an IQ greater than 80 such that he will not choose to be greedy on the first round either to maximise his own profit. And in this question always bear in mind that you do not care about the other person  all you want is to maximise your own profit.
If you are not greedy the first round and he is not either, then each earns $3. Repeat until the first scenario described occurs.
In this solution set, it is inevitable that you will get equal or less money than the opponent. However, it maximises the profit that YOU get, not caring how much the other person gets as that is none of your concern; therefore it is necessarily the best solution.
However, a better way would be for the two players to communicate and agree on constantly choosing not to be greedy. The question, though, does not allow this to happen as it disallows communication between the two parties.
Therefore, just choose not to be greedy as long as the other person does the same, and choose to be greedy the instant the other person does so to get the maximum amount of cash.
Note however that if the other person ever chooses to be not greedy after a long $1$1 stalemate, you should instantly switch to being not greedy if possible

Posted by Jack Lim
on 20060302 08:25:53 