Paths to stability in two-sided matching with uncertainty

We consider one-to-one matching problems under two modalities of uncertainty that differ in the way types are assigned to agents. Individuals have preferences over the possible types of the agents from the opposite market side and initially know the name but not the type of the other players. Learning occurs via matching and using Bayes' rule. We introduce the notion of a stable and consistent outcome, and show how the interaction between blocking and learning behavior shapes the existence of paths to stability in each of the uncertainty environments. Existence of stable and consistent outcomes then follows as a side result.