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Wei_Dai comments on AI cooperation in practice - Less Wrong
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Suppose we have two possible actions X,Y and A prefers <X,Y> to <Y,X> to <X,X> to <Y,Y> and B prefers <Y,X> to <X,Y> to <X,X> to <Y,Y>. What will be the outcome if both of them use main4() with their respective orderings and the same proves() function?
Probably <X,X>, which is not quite optimal. This doesn't solve the bargaining problem, which is exactly what your example is.