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fractalman comments on Robust Cooperation in the Prisoner's Dilemma - Less Wrong
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trollDetector-a fundamental part of psychbot-gets both of these to cooperate.
TrollDetector tests opponents against DefectBot. If opponent defects, it cooperates. if opponent cooperates, TrollDetector defects.
So both UnfairBot and Fairbot cooperate with it, though it doesn't do so well against itself or DefectBot.
TrollDetector is not a modal agent.
hm. I'm still a bit shaky on the definition of modal agent...does the following qualify?
IF(opponentcooperates with me AND I defect is a possible outcome){defect} else{ if (opponent cooperates IFF i cooperate) (cooperate){else defect}
(edit: my comment about perfect unfair bots may have been based on the wrong generalizations from an infinite-case). addendum: if what I've got doesn't qualify as a model agent I'll shut up until I understand enough to inspect the proof directly.
addendum 2: well. alright then I'll shut up.
What do you even mean by "is a possible outcome" here? Do you mean that there is no proof in PA of the negation of the proposition?
The formula of a modal agent must be fully modalized, which means that all propositions containing references to actions of agents within the formula must be within the scope of a provability operator.