People may be surprised to notice certain regularities that hold in existing knowledge they have had for some time. That is, they may learn without getting new factual information. We argue that this can be partly explained by computational complexity. We show that, given a knowledge base, finding a small set of variables that obtain a certain value of R 2 is computationally hard, in the sense that this term is used in computer science. We discuss some of the implications of this result and of fact-free learning in general.

We formulate a notion of stable outcomes in matching problems with one-sided asymmetric information. The key conceptual problem is to formulate a notion of a blocking pair that takes account of the inferences that the uninformed agent might make. We show that the set of stable outcomes is nonempty in incomplete-information environments, and is a superset of the set of complete-information stable outcomes. We then provide sufficient conditions for incomplete-information stable matchings to be efficient. Lastly, we define a notion of price-sustainable allocations and show that the set of incomplete-information stable matchings is a subset of the set of such allocations.