Click the link to learn the background, but briefly ...
In what’s a sort of a social experiment for the classroom, the teacher proposes this offer for extra credit on the final paper:
Here you have the opportunity to earn some extra credit on your final paper grade. Select whether you want 2 points of 6 points added onto your final paper grade. But there’s a small catch: if more than 10% of the class selects 6 points, then no one gets any points. Your responses will be anonymous to the rest of the class, only I will see the responses.
So basically, if the individual acts good for the group, everyone gets extra credit. However, if enough students act selfishly — or smartly, some might argue — no one benefits. Greed trumps good. The Tragedy of the Commons.
I ask for 6 points. My reasoning is that if everyone gets 2 points, the point spread remains the same and extra points are meaningless. It is possible that everyone (or less than 10%) will also choose 6 in which case I'm ahead 4.
If the class colludes (which the rules do not forbid) I will agree to ask for 2 but I'll still choose 6.
My thinking was the same. I would select 6 points. I think that is also the correct answer according to game theory.
I guess it sort of depends how the grading works, but no reason to ask for 2 points if they are grading on a curve. If everyone gets it your relative grade stays the same anyway. It's all relative anyway, right? If you select 2 it can't help you but could hurt you. If you select 6, it can't hurt you but could help you. Besides, even if it isn't relative, 2 points is like trying to bribe me with a dime. It's not really worth it to me.
Last edited by Anaxagoras on Sat Jul 18, 2015 1:10 am, edited 1 time in total.
A fool thinks himself to be wise, but a wise man knows himself to be a fool.
William Shakespeare
My thinking was the same. I would select 6 points. I think that is also the correct answer according to game theory.
I guess it sort of depends how the grading works, but no reason to ask for 2 points if they are grading on a curve. If everyone gets it your relative grade stays the same anyway. It's all relative anyway, right? If you select 2 it can't help you but could hurt you. If you select 6, it can't hurt you but could help you. Besides, even if it isn't relative, 2 points is like trying to bribe me with a dime. It's not really worth it to me.
I'm not sure game theory accepts that as an optimal solution--after all, if everyone follows the "optimal" solution, nobody wins anything.
Spoiler:
IIRC, the best considered solution is setting up a random element that selects your choice for you. Since there is no winning individual strategy, you maximize your winnings by setting up that there is an X% chance that you will pick 6 vs. 2. Then you pick X so that the expected payout overall is maximized if everyone picks the same X.
Of course, even though it counts in game theory as an optimal solution that everyone can reach without collusion, nobody's going to do that much math, so it's all screwed anyway.
"If fighting is sure to result in victory, then you must fight! Sun Tzu said that, and I'd say he knows a little bit more about fighting than you do, pal, because he invented it, and then he perfected it so that no living man could best him in the ring of honor. Then, he used his fight money to buy two of every animal on earth, and then he herded them onto a boat, and then he beat the crap out of every single one. And from that day forward any time a bunch of animals are together in one place it's called a zoo! (Beat) Unless it's a farm!"
--Soldier, TF2
