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 best for BOTH players is of course being not greedy. Over a large number of games we can assume that this equilibrium will be reached. Every time one of the players will get greedy he will earn more, but then he might expect a retaliation of greed by the other one, which will cost him his previous earnings.
It is better to be greedy only if the other player will greedy/not greedy all the time regardless of what you do. But this kind of behaviour can be considered stupid, since it reduces his earnings, so we can rule it out.

Posted by Yuval on 2006-06-17 09:29:29