Ex-ante efficient matching
Any ex ante efficient and group strategyproof mechanism for a standard matching problem is a sequential dictatorship. The set of standard matching problems comprises marriage markets, housing markets and roommate problems. For all three the results holds whether or not the agents may have outside options. A mechanism is ex ante efficient if there exists no distribution over types and costly learning technology such that all agents are at least as well off if a different mechanism was used in the same environment. In a sequential dictatorship a first dictator chooses their match. Depending on the problem this match is a spouse, a house, a roommate or the outside option. Then another agent, the second dictator gets to choose their match. The sequence of dictators may depend on all preceding choices. The mechanism is slow in the sense that all agents may delay learning until they get to make a choice.
All six problems are covered by the same basic proof.