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Will_Sawin comments on Malice, Stupidity, or Egalité Irréfléchie? - Less Wrong
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Well, their problem is not opposing interests. In your model, they seem to have the same interests - they're just at the wrong Nash equilibrium.
Right, it's definitely not PD. And it's not Chicken. As you say, it's one with two Nash equilibria, a good one at both-cooperate and a worse one at both-defect. I just don't remember what it's called and don't know where to find out online.