Xkcd Game Theory Question

The truly strategic player would do research on the final exam ahead of time, pool together class resources and just hire someone to sign up for the course to take the loss.

Unfortunately, I think this is not an equilibrium strategy. An equilibrium strategy profile is one where, given everyone is using that strategy, no single individual cannot profitably deviate. But if I know everyone else in the class is going to use this strategy, and I draw the short straw (and assuming for simplicity that nobody else can draw the short straw), then I know everybody else will answer 10, and I maximize my chance of winning by choosing x such that ((n-1)10 + x) / n) + 10 = x.

But I wonder if this or a similar strategy would provide the maximum expected reward for the group*. In that case, then there's a situation that is somewhat like a multi-player prisoner's dilemma, in that if everybody always "cooperated", they'd all be better off in the long run. Yet whoever draws the short straw is better off not cooperating. Therefore nobody cooperates.

In the case of repeated one-on-one games (where you play the same game with the same player multiple times), there is a solution to the prisoner's dilemma: strategies like "tit for tat" where you can essentially punish people for non-cooperation (as described in fantastic classic "The Evolution of Cooperation" by Robert Axelrod). But since there are multiple people in the class, this is more like a a multi-player prisoners dilemma (as described by Thomas Schelling in "Micromotives and Macrobehavior"), or a "collective action" problem. These can also be solved if you go "outside" the game and have systems for punishing people who don't cooperate (e.g. union members beating up scabs).

Another thing about Schelling points: a "strategy" can be a Schelling point. It is unlikely that the whole class would independently do the same analysis and come up with the same strategy (even if it was an equilibrium strategy). But if you stood up before the class and explained the strategy before the exam, it would become a Schelling point.

but everyone has to cooperate here, if a few guys go crazy and say some super outlandish number to shift the average then all bets are off. Hence my most common pet-peeve with data .. median not average.

  If everyone follows this strategy, then I will win if exactly one person draws the short straw and if that one person isn't me. The former has a probability that rapidly approaches 1/e≈36.8% as n increases