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SoullessAutomaton comments on Timeless Decision Theory: Problems I Can't Solve - Less Wrong
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Meaningful results would probably require several iterations of the game, though, with different players (also, the expected loss in my scenario was $5 per game).
I seem to recall Douglas Hofstadter did an experiment with several of his more rational friends, and was distressed by the globally rather suboptimal outcome. I do wonder if we on LW would do better, with or without Eliezer?