This paper studies a stability notion and matching processes in the job market with incomplete information on the workers' side. Each worker is associated with a type, and each firm cares about the type of her employee under a match. Moreover, firms' information structure is described by...

Predictions under common knowledge of payoffs may differ from those under arbitrarily, but finitely, many orders of mutual knowledge; Rubinstein's (1989)Email game is a seminal example. Weinstein and Yildiz (2007) showed that the discontinuity in the example generalizes: for all types with...