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.

well...
the biggest problem here is the statement: "Assume that your opponent doesn't necessarily use the same strategy as you"

and how it relates to: "playing an unknown finite number of games"

The best strategy is of course that both players always are not greedy. This is because the total of 6$ given out is the most possible of all 4 options.

And since it is the best strategy and it has been assumed that: "Both players are trying to get as much money as possible". Then It is the option you should choose 1st.

Now given the strategy underlined above, if you knew you were only playing once, you might then choose greedy and take advantage of your 'competitor's' good will as it were.

But then of course you would have to assume that the other would have had the same thought, and not wanting them to leave you with 0$ you still have to stick with greedy.

At which point you would have the same realization that they would have, and prefering 3$ to 1$ dollars, you would change your choice back to not greedy.


However, this best solution would assume that indeed the other player would use the same strategy, which isn't a problem as far as i can tell from the quote above.


notes:

there is no reason to try and outwit the other player by employing any strategy other than always not guilty.. otherwise, with your possible outcomes being 0$ 1$ 3$ and 5$ your average take would be 9/4$ and the opponens would be the same... over time it wouldnt be worth it... greed never is

Posted by wastoids on 2005-12-20 22:53:06