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.