A college professor posed a dilemma on students’ final exam: Choose to get either 6 points or 2 points of extra credit. Here’s the catch: If more than 10 percent of the class chooses 6 points of extra credit, nobody gets any extra credit at all. Otherwise, everybody gets what they chose.
Quinn Kelley has the story in the Baltimore Sun about Dylan Selterman’s class at the University of Maryland, College Park. The dilemma is a slight variation on the famous game-theory quandary known as the “prisoner’s dilemma” or sometimes the “tragedy of the commons.” The game has been used in several instances throughout history, including to study the possible results of nuclear war.
The classic prisoner’s dilemma involves only two players. The sucker’s payoff, which is what a player who decides to cooperate gets when the other player defects and gets away with it, is typically less than the penalty that both players receive if they both decide to go for the big prize, known as the temptation.
In this case, since grades are involved, I suppose Mr Selterman couldn’t make the sucker’s payoff less than zero, resulting in a game variant that’s not the most common form of the prisoner’s dilemma. The tool has been studied for some time as an insight into human nature and the spirit of cooperating with other parties whose moves you may not be able to predict.
Also, a typical prisoner’s dilemma game would involve multiple iterations, so that players could learn from their mistakes. This one had just one iteration.
How would you play? With the way the game is set up and knowing what the payoffs are, I can’t see any reason not to go for the 6. Basically, I’ll get no extra credit if more than 10 percent of the class chooses 6, no matter what I choose for myself. So whether I choose 2 or 6, I’ll get zero if the class doesn’t cooperate. I might as well choose 6, since I can’t manipulate the class in a one-iteration game.
That’s why this game in class differs from the classic prisoner’s dilemma. The sucker’s payoff, +2 here, is supposed to be less than the penalty all students would suffer if too many of them defect, which is +0. Players would then be driven to defect, which is what the game is supposed to teach.
The lesson is you can’t do any worse than not trusting your opponent. Why do you think we built up such a large nuclear arsenal ourselves during the Cold War?
Source: Anatol Rapoport and Albert M Chammah. Prisoner’s Dilemma. Ann Arbor, Mich.: The University of Michigan (Dec 15, 1965).
