I asked the students to make more or less the same decision faced by the actors in the formal model discussed in that lecture, though their choice was bit simpler because only one of the actions involved risk.
The optimal strategy here was not to cooperate at all, since the expected utility for cooperating with any given state is 0.8 (0.4*2 + 0.6*0) and choosing not to cooperate brings 1 point for certain.
Because didn’t want a repeat of the near-revolt that resulted from the last activity, I decided to talk through the optimal strategy at this point. That did them no good in terms of the outcome of the first half of the activity, but helped ensure that everyone made the best choice possible in the second half. Unsurprisingly, I found that many of them identified the correct strategy here but for the wrong reason. They thought the reason that it was unwise to cooperate with any of the states was because the probability that they’d cooperate back was less than 0.5. Only a handful were thinking in terms of expected utilities. So I then re-explained what those are, how they’re calculated, and why you’re always better off thinking in those terms than using simple heuristics based on raw probabilities (or under best case/worst case logic, for that matter).
I then used an online number generator to determine which of the five countries, if any, were willing to cooperate with those who had A cooperate with them. As it happens, B and C did, which of course means 40% of the countries cooperated, as we’d expect given a probability of 0.4. So those who behaved optimally did better than those who cooperated with every country. However, there were some students who did even better still. A small number chose, for whatever serendipitous reason, to cooperate with B and C but no other country. These very lucky students earned 7 points.
In the second half, I had them make a very similar decision with just two small (but crucial) details changed. On the second run, I told them that the probability of any given state cooperating with them had dropped to 0.2, but the value of mutual cooperation had increased to 10 points. That changes the optimal strategy from cooperating with none to cooperating with all, since the expected utility from attempting cooperation with any given state is now 2 points (0.2*10 + 0.8*0). As expected, most of them chose to cooperate with all five states this time, as they should.
And I think some of them even grasped that this helps them understand why we saw in the lecture they were to have listened to ahead of time that trust is a stronger predictor of whether states cooperate with one another economically when the potential benefits of cooperation are low, but has no effect once the stakes get high, since even states that don’t trust one another much are willing to take a risk when the upside is huge.
Unfortunately, at this point, the internet cut out. So I was unable to draw random numbers for the second part. None of the students could get online using their phones, laptops, or tablets either. So that was nice and embarrassing. Didn’t make me feel like an amateur at all. I told them we’d assume one country cooperated back, so those who cooperated with all got 10 points and those with none got 5. (This time around, they realized that it didn’t make much sense to pick and choose.) Next time, I’m bringing my laptop to class and using Stata to generate random numbers instead of the internet.