"And are you really "exploiting" an "irrational" opponent, if the party "exploited" ends up better off? Wouldn't you end up wishing you were stupider, so you could be exploited - wishing to be unilaterally stupider, regardless of the other party's intelligence? Hence the phrase "regret of rationality"..."
Plus regret of information. In a mixed population of classical decision theory (CDT) agents and Tit-for-Tat (TFT) agents, paired randomly and without common knowledge of one another's types, the CDT agents will imitate the TFT agents until the final rounds, even when two CDT agents face each other. However, if the types of the two CDT agents are credibly announced then they will always defect and suffer great losses of utility.
Followup to: The True Prisoner's Dilemma
For everyone who thought that the rational choice in yesterday's True Prisoner's Dilemma was to defect, a follow-up dilemma:
Suppose that the dilemma was not one-shot, but was rather to be repeated exactly 100 times, where for each round, the payoff matrix looks like this:
As most of you probably know, the king of the classical iterated Prisoner's Dilemma is Tit for Tat, which cooperates on the first round, and on succeeding rounds does whatever its opponent did last time. But what most of you may not realize, is that, if you know when the iteration will stop, Tit for Tat is - according to classical game theory - irrational.
Why? Consider the 100th round. On the 100th round, there will be no future iterations, no chance to retaliate against the other player for defection. Both of you know this, so the game reduces to the one-shot Prisoner's Dilemma. Since you are both classical game theorists, you both defect.
Now consider the 99th round. Both of you know that you will both defect in the 100th round, regardless of what either of you do in the 99th round. So you both know that your future payoff doesn't depend on your current action, only your current payoff. You are both classical game theorists. So you both defect.
Now consider the 98th round...
With humanity and the Paperclipper facing 100 rounds of the iterated Prisoner's Dilemma, do you really truly think that the rational thing for both parties to do, is steadily defect against each other for the next 100 rounds?