Can you write the “cooperate iff I cooperate iff they cooperate … ” bot this way?
This can be unpacked as an algorithm that searches for a proof of the statement “If I cooperate, then my opponent also cooperates; if I defect, then my opponent also defects”, and if it finds its proof, it cooperates. Under certain conditions, two players running something like this algorithm will cooperate. As you can see, agent’s decision here depends not on the opponent’s decision, but on the opponent’s decision’s dependence on your decision (and not dependence on the dependence of your decision on the opponent’s decision, etc.).
Okay. I think that fits with my view: so long as it’s possible to go from X’s strategy and Y’s strategy to an outcome, then we can build a table of strategy-strategy-outcome triplets, and do analysis on that. (I built an example over here.) What I’m taking from this subthread is that the word “strategy” needs to have a particular meaning to be accurate, and so I need to be more careful when I use it so that it’s clear that I’m conforming to that meaning.
This can be unpacked as an algorithm that searches for a proof of the statement “If I cooperate, then my opponent also cooperates; if I defect, then my opponent also defects”, and if it finds its proof, it cooperates. Under certain conditions, two players running something like this algorithm will cooperate. As you can see, agent’s decision here depends not on the opponent’s decision, but on the opponent’s decision’s dependence on your decision (and not dependence on the dependence of your decision on the opponent’s decision, etc.).
Okay. I think that fits with my view: so long as it’s possible to go from X’s strategy and Y’s strategy to an outcome, then we can build a table of strategy-strategy-outcome triplets, and do analysis on that. (I built an example over here.) What I’m taking from this subthread is that the word “strategy” needs to have a particular meaning to be accurate, and so I need to be more careful when I use it so that it’s clear that I’m conforming to that meaning.