Silas Barta has a good takedown of this goofy blog post from an economics professor, Daniel Hamermesh, and his attempt to impart the lessons of economics to his students:

Each year in my 500-student principles class I gather a group of eight students and tell them that I will auction a $20 bill to the highest bidder. If two or more students bid the same thing, the difference between $20 and their joint bid will be divided among the winning bidders. They can collude to fix the price just like oligopolists who violate antitrust laws, but they must mark down their bids in secret.

Today seven of the students stuck to the collusive agreement, and each bid $.01. They figured they would split the $20 eight ways, netting $2.49 each. Ashley, bless her heart, broke the agreement, bid $0.05, and collected $19.95. The other 7 students booed her, but I got the class to join me in applauding her, as she was the only one who understood the game.

No one disputes that the collusive agreement does not constitute a Nash equilibrium. No one disputes that, with no other mechanisms in place, it might be naive to assume that everyone would follow through with an agreement, especially as the number of players increased.

But so what? The parts I put in bold above do not follow from pure game theoretic considerations. There is nothing that says we ought to bless or congratulate others for playing a narrowly defined best response; indeed, if you want to go that route, we should be chastising her because it's in each of our narrow self-interest to make everyone else feel guilty for defecting in cases like this. So this professor can't have it both ways: He wants to be "non-selfish" by congratulating someone else for something that doesn't help him personally, and yet the very thing he is congratulating is the student's unwillingness to be so gracious herself.

I realize I may sound wishy washy and anti-rigorous here; let me assure the casual reader that I "get" game theory. It was my field (analogous to a major) at NYU, the program of which was renowned for its bona fides in this area. The professor telling the above anecdote fits the stereotype that other social scientists have of economists. Economists defend themselves and say, "Hey, our discipline doesn't tell people to be selfish; we just view the world as it is, not as the sociologists want it to be." But no, Hamermesh just gave the game away. He was applauding a student for reneging on an agreement in order to benefit herself and screw over her classmates. Moreover, he implies that the other students were stupid and that's the only reason they too didn't try to stab each other in the back. It wasn't that they were naive or too trustworthy; nope, they must not have understood the game.

For what it's worth, I too used a technique similar to this, when I taught cartels in microeconomics. I would show the class $50 in cash, and say:

OK everyone, I want you to take out a small slip of paper, and put your name on one side. Then on the other side, without letting anyone else see, write a "C" or "D." Then fold it up, and I'll collect them. Then I'll go through and show the class the letters one at a time. After it's all done, here's what I'll do: If there are all Cs, then you all split the money evenly. [There would normally be about 20 kids in the room.] If there is one D, that person gets $40 him or herself, and everyone else gets nothing. If there are two Ds, they each get $15 and everyone else gets nothing. If there are 3 Ds, they each get $8. Finally, if there are 4 or more Ds, nobody gets anything. I'm going to leave the room for 10 minutes and let you discuss it, and then when I come back I want you to write your answer. Don't write your answer until I come back. Last thing, I won't ever reveal who the people writing 'D' were. I will pay them outside of class.

What's interesting is that I almost never had to pay any money; in fact I think maybe I never paid any, but I'm not sure. However, after a few semesters of this pattern, I switched it up and used bonus points on the next exam as the reward. The payoff structure was the same: It was weakly dominant (note not strictly dominant, and hence this actually wasn't a true prisoner's dilemma) to write a D, because there were scenarios where that would garner you more bonus points, and it would never hurt you to write D. And yet just about always, everyone in the class wrote C when it was points, not money. Presumably this was due to (a) kids felt worse about stealing points from their friends, and (b) the football players threatened to literally beat up defectors when there were exam points on the line.

Anyway, my problem isn't with Hamermash's use of a game to keep the class interested. My problem is with him applauding students for defecting, and telling them that's the right thing to do. Does Hamermash leave a tip in a restaurant when he's on a road trip at a place he's not likely to visit again within a year? If so, what a moron! He clearly doesn't understand the rules of restaurant pricing.

(For more on the problems with typical popularizing of game theory, see my article complaining about Hal Varian's discussion of the movie A Beautiful Mind.)

UPDATE: I used to put this as a bonus question on the next exam, so I'll do it here as well, inasmuch as there are some serious econ geeks who frequent these pages: There actually exists a Nash equilibrium in which I pay out money, given the rules described above. So if a class of students had realized it and assigned people the various strategies to play, it would be self-enforcing, at least if we assume that each kid only cares about maximizing how much money he or she gets from me. What is the equilibrium?