College Game Theory

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Rob Lister
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College Game Theory

Post by Rob Lister » Fri Jul 17, 2015 3:58 pm

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.
http://q13fox.com/2015/07/16/is-this-th ... r-offered/

My answer
Spoiler:
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.

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Re: College Game Theory

Post by Abdul Alhazred » Fri Jul 17, 2015 4:14 pm

There have been extensive computer simulations of this sort of thing by the Rand Corporation back in the 1950s. I'll look up some evidences later in case anyone cares.

Bottom line: You will come out ahead in the long run if you always act selfishly and gamble on the other guy choosing to be a chump for whatever reason.
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Re: College Game Theory

Post by Anaxagoras » Fri Jul 17, 2015 11:03 pm

Spoiler:
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.
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Re: College Game Theory

Post by Rob Lister » Fri Jul 17, 2015 11:23 pm

Um ... you like supposed to like use spoiler tags like.

I would certainly attempt to collude though. It's the smart thing to do. I'd be all sincere too.

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Re: College Game Theory

Post by Anaxagoras » Sat Jul 18, 2015 1:13 am

Oh, well OK.

Here's how I would tweak it to make it more interesting:
Spoiler:
The 2-pointers get their two points no matter what, but the 6-pointers get zero if too many people choose 6.
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Re: College Game Theory

Post by Abdul Alhazred » Sat Jul 18, 2015 1:24 am

An entirely different game illustrating an entirely different principle.
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Re: College Game Theory

Post by Rob Lister » Sat Jul 18, 2015 10:28 am

Anaxagoras wrote:Oh, well OK.

Here's how I would tweak it to make it more interesting:
Spoiler:
The 2-pointers get their two points no matter what, but the 6-pointers get zero if too many people choose 6.
That is an evil tweak.
Spoiler:
Plus I could not collude with fraudulent intent. Everybody would have to choose 2. Knowing that I still might choose 6 because I've got a pair.

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Re: College Game Theory

Post by gnome » Tue Jul 21, 2015 3:29 am

Anaxagoras wrote:
Spoiler:
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.
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