A version of the Second Fundamental Theorem of Welfare Economics that applies to a money-free environment, in which a set of indivisible goods needs to be matched to some set of agents, is established. In such environments, 'trade' can be identified with the set of hierarchical exchange...

The study of matching problems typically assumes that agents precisely know their preferences over the goods to be assigned. Within applied contexts, this assumption stands out as particularly counterfactual. Parents typically do invest a large amount of time and resources to find the best...