Comment by anastasds | Hacker News Reader

Comment by anastasds | Hacker News Reader

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.

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].

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.

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.... and it gives some further citations.

All students get 2 points automatically, and the outcomes are +4, 0, and -2. That satisfies your demand for a negative outcome (and shows that your demand is unnecessary)

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