Fairness and group-strategyproofness clash in assignment problems
No group-strategyproof and ex-post Pareto optimal random matching mechanism treats equals equally. Every mechanism that arises out of the randomization over a set of non-bossy and strategyproof mechanisms is non-bossy. Random serial dictatorship, which arises out of a randomization over all deterministic serial dictatorships is non-bossy but not group-strategyproof.