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Wei_Dai comments on Timeless Decision Theory: Problems I Can't Solve - Less Wrong
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I want to note that this is also know in Cooperative Game Theory as an "empty core". (In Social Choice Theory it's studied under "majority cycling".) See http://www.research.rmutp.ac.th/research/Game%20Theory%20and%20Economic%20Analysis.pdf#page=85 for a good explanation of how Cooperative Game Theory views the problem. Unfortunately it doesn't look like anyone has a really good solution.