= 27d567bc2d48d9f40e9ccc20ea370b15)
thomblake comments on The Truly Iterated Prisoner's Dilemma - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (85)
In the case where you know N rounds will occur, you can reason as follows:
If one cannot be punished for defection after round x, then one will defect in round x. (premise)
If we know what everyone will do in round x, then one cannot be punished for defection in round x. (obvious)
There is no round after N, so by (1) everyone will defect in round N.
if we know what everyone will do in round x, then we will defect in round x-1, by (1) and (2).
By mathematical induction on (3) and (4), we will defect in every round.
If everyone doesn't know what round N is, then the base case of the mathematical induction does not exist.
The unexpected hanging paradox makes me sceptical about such kinds of reasoning.
I'm not sure why that should apply. The unexpected hanging worked by exploiting the fact that days that were "ruled out" were especially good candidates for being "unexpected". Other readings employ similar linguistic tricks.
The reasoning in the first case does not work in practice because in a tournament premise (1) is false; tit-for-tat agents, for example, will cooperate in every round against a cooperative opponent.
But that is not even relevant to the fact that the mathematical induction does not work for unknown numbers of rounds.