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DefectiveAlgorithm comments on A simple game that has no solution - Less Wrong
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P1: .5C .5B
P2: Y
It's not a Nash equilibrium, but it could be a timeless one. Possibly more trustworthy than usual for oneshots, since P2 knows that P1 was not a Nash agent assuming the other player was a Nash agent (classical game theorist) if P2 gets to move at all.
I think this should get better and better for P1 the closer P1 gets to (2/3)C (1/3)B (without actually reaching it).