All of Woett's Comments + Replies

I'm confused about defection becoming a dominant strategy.. Because the existence of a dominant strategy suggests to me that there should exist a unique Nash equilibrium here, which is not the case. Everyone defecting is a Nash equilibrium, but 50 people cooperating and 49 defecting is a Nash equilibrium as well, and a better one at that. Something (quite likely my intuition regarding Nash equilibria in games with more than 2 players) is off here. Also, it is of course possible to calculate the optimal probability that we should defect and I agree with Fee... (read more)

5DanielVarga9y
Nice. If we analyze the game using Vitalik's 2x2 payoff matrix, defection is a dominant strategy. But now I see that's not how game theorists would use this phrase. They would work with the full 99-dimensional matrix, and there defection is not a dominant strategy, because as you say, it's a bad strategy if we know that 49 other people are cooperating, and 49 other people are defecting. There's a sleight of hands going on in Vitalik's analysis, and it is located at the phrase "regardless of one’s epistemic beliefs [one is better off defecting]". If my epistemic belief is that 49 other people are cooperating, and 49 other people are defecting, then it's not true that defection is my best strategy. Of course, Vitalik's 2x2 matrix just does not allow me to have such refined epistemic beliefs: I have to get by with "attack succeeds" versus "attack fails". Which kind of makes sense, because it's true that I probably won't find myself in a situation where I know for sure that 49 other people are cooperating, and 49 other people are defecting, so the correct game theoretic definition of dominant strategy is probably less relevant here than something like Vitalik's "aggregate" version. Still, there are assumptions here that are not clear from the original analysis.