The Dirty Face Problem with Unawareness

By revisiting the classic dirty-face problem we highlight the notion of `unawareness' (a simpler state space) and compare it with `impreciseness' (a coarser information partition). The outcomes are derived with various information structures. That allows us to 1) demonstrate a model of differing interpretations of public information using asymmetric awareness; 2) compare and contrast the impact of unawareness and impreciseness on learning; 3) analyze the value of awareness and the value of preciseness; and 4) demonstrate the effect of unawareness and impreciseness on information revelation with indirect aggregation.