
Student’s Dilemma, a riff of the Prisoner version with extra credit - valleyhut
http://flowingdata.com/2015/07/10/students-dilemma-a-riff-of-the-prisoner-version-with-extra-credit/
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egillie
Is the class still curved? Because if so, then choosing 6 points would always
be the correct strategy.

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jmmcd
SPOILER?

The "correct" answer is to generate a random number in [0, 1]. If less than
0.1, then select 6, else select 2. For safety use 0.05 (say) instead of 0.1.
This means that everyone is guaranteed 2, but some (as many as possible) get
6. It works without coordination.

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mikexstudios
Except that you need to coordinate everyone to use the random number generator
system...

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jmmcd
Everyone can work that out for themselves! In theory. Or else remember it from
the course textbook. In context, "coordination" usually means communication
after the game is set up, whereas the idea of the random number generator is a
standard approach even in advance.

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ableal
> What's your answer? I take the two.

Any guesses about where (in society) one can find those who answer "I take the
six"?

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michaelt
At schools that do forced-curve grading or grade normalisation. If what
matters is your relative rank in the class, rather than your absolute score,
then "everyone takes the 2" and "everyone takes the 6" produce the same
relative ranks for everyone - i.e. the same result for you - while "you take
the 2 while some other people take the 6" reduces your relative rank.

If there's a nonlinearity introduced by the mapping from points to a letter
grade to a GPA, and you have an extremely detailed knowledge of your current
grades, and you know 2 points won't bump you up a letter grade whereas 6
points will (i.e. 2 points and 0 points have the same effect on your GPA, only
6 points will improve your GPA).

Among people who believe punishing defectors to produce fair outcomes is more
important than producing the best average outcome. If you believe there are
inevitably people who will take the 6 points, and those people are assholes,
and you'd rather punch an asshole in the face (make them lose 6 points) even
if it hurts your hand (you lose 2 points). The same logic that makes people
brake for tailgaters.

In parts of society that prize 'rational self interest' and believe everyone
should look out for their own best interests and let market forces sort it
out; or that it's inevitable that other people will do this and if you're not
doing it, you're basically a sucker. The same logic that makes people take
seven-figure salaries in finance instead of becoming school teachers - and
makes salesmen push the product with the highest commission, not the one
that's best for the customer.

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JesperRavn
To clarify, the theory behind the free market is that the seven figure salary
in finance represents a greater contribution to the net social good than a
teacher. You personally might not agree with this, but you are completely
misrepresenting economic theory when you say that proponents of the free
market consider it to be a prisoners dilemma situation. On the contrary they
argue for the free market precisely because they believe that in the free
market, individual and social goals are aligned

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anastasds
All of this is poorly defined (edit: I meant mathematically not well defined)
as a game theory problem, from the premises to the suggestion that it's "the
prisoner's dilemma with extra credit".

First, the prisoner's dilemma is defined for two people, which this is not.
Furthermore, the prisoner's dilemma assumes perfectly rational actors; we
cannot assume that of students.

Second (and related to the number of players), the 10% metric has different
meanings based on the number of players (students). With two people, one
person opting for six points constitutes 50%, which might be the case for an
advanced elective at a small school. A first year biology class at a major
university might have hundreds of students, in which case we can treat the 10%
condition as stated.

Third, the outcomes of the prisoner's dilemma are either absolute gain or
absolute loss - either jail or freedom. In this case, no possible outcome
constitutes loss relative to the starting state; a player can fail to gain,
but cannot be worse from where he or she started before playing. A premise
that would make this closer to the prisoner's dilemma would be that if more
than some percentage of the students opt for the six points, then all students
lose six points.

Overall, this seems like something this instructor is doing for fun rather
than as an experiment in a formal extension of the prisoner's dilemma.

For my part, I'd opt for the 2, based on what I remember about undergraduate
students. I have no formal reasoning to support this, however.

tl;dr As stated, this is neither an extension of the prisoner's dilemma, nor
is it well-defined in any case. It seems to me that any suggested solution
will require either additional data or additional assumptions. Either way, I'd
choose 2 points, and I would be interested to see the outcome of this
instructor's survey.

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jmmcd
I'm afraid you need to re-read your notes :)

N-player prisoner's dilemma is well-known. Neither 2-player nor N-player
assumes rational actors. EDIT: It assumes that payoffs are in a reasonable
unit of utility (so we don't need to think about whether $1000 is worth 10
times as much as $100, or more, or less). That's a related point but not the
same.

The second point doesn't make it undefined. If there are two people, and one
opts for 2 points, then the 10% is exceeded and the condition is triggered. No
confusion.

The prisoner's dilemma arises just as well if the payoff matrix is all
positive. You just need T > R > P > S
[[https://en.wikipedia.org/wiki/Prisoner%27s_dilemma](https://en.wikipedia.org/wiki/Prisoner%27s_dilemma)].

~~~
anastasds
From your link,

>The prisoner's dilemma is a canonical example of a game analyzed in game
theory that shows why two purely "rational" individuals might not cooperate,

The generalized prisoner's dilemma is indeed well-known; the name "prisoner's
dilemma", without further qualification, does, however, refer to the case of
two perfectly rational players (hence the title of the wiki article you
linked). In either case, the generalized prisoner's dilemma generalizes the
payoffs and penalties, but still assumes two players.

Perhaps you were thinking of the iterated prisoner's dilemma since it does
deal with more than two players; however, the iterated prisoner's dilemma
deals with playing the game more than once in succession, while here we have a
single round with an unknown number of players.

As it stands, the given problem is not a version of the prisoner's dilemma,
but an entirely different sort of problem altogether. We could perhaps impose
additional constraints in order to reduce it to some generalization of the
prisoner's dilemma; in any case, as stated, we cannot say that this is "the
prisoner's dilemma with extra credit" in any meaningful sense.

(significantly edited for clarity and organization)

Further edit: I am not aware of a canonical statement and solution of an
N-player prisoner's dilemma. I would be interested in a reference.

~~~
jmmcd
The players don't have to be rational. It is interesting to study PD with non-
rational players, e.g. when it arose as a model of the nuclear arms race. It's
true that the PD _also_ "shows why two purely 'rational' individuals might not
cooperate" but that is not part of the defn of PD.

I was not confusing iterated and n-player versions.

For a ref, eg
[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.29....](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.29.388&rep=rep1&type=pdf)
and it gives some further citations.

