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Squark comments on A simple game that has no solution - Less Wrong
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I suspect that UDT players always reach the Nash bargaining solution although I have no proof.
For this game I proved that there is a local maximum of the Nash product when 1 plays B with probability 3/8 and C with probability 5/8 and 2 plays Y. I'm not sure whether it's global (can the Nash product have non-global local maxima?)