An exam with cheating allowed

Statistical decision theory is about making decisions in the presence of uncertainty. We can’t know everything, but we still need to make choices.  In decision theory we assume that the world isn’t out to get us — if cigarette smoke is toxic, it is so regardless of whether or not we study it, and whether or not we’re trying to stamp it out. Murphy’s Law is true, but only as an engineering design principle, not a fact about the malevolence of Nature.

Game theory is the evil twin of decision theory — it’s about making choices in the presence of competition, when the other players aren’t precisely out to get you, but they are out to do the best for themselves.  There are a few examples of game theory in medical statistics: how do you set up regulations so that making effective drugs is more profitable than making ineffective ones? how do you use new antibiotics, given that resistance will inevitably develop? Typically, though, game theory works best in ecology, where natural selection ensures that organisms behave as if they were trying to maximise their numbers of descendants given the behaviour of other organisms.

A UCLA professor teaching a course in behavioural ecology decided to try to make his students really appreciate the problems of cooperation and competition that arise in game theory:

A week before the test, I told my class that the Game Theory exam would be insanely hard—far harder than any that had established my rep as a hard prof.  But as recompense, for this one time only, students could cheat. They could bring and use anything or anyone they liked, including animal behavior experts. (Richard Dawkins in town? Bring him!) They could surf the Web. They could talk to each other or call friends who’d taken the course before. They could offer me bribes. (I wouldn’t take them, but neither would I report it to the Dean.) Only violations of state or federal criminal law such as kidnapping my dog, blackmail, or threats of violence were out of bounds.