Consider the following game of incomplete in- formation played by a worker (W) and a firm (F). The worker has private

information about her level of interest in the job. With probability 1/4, she is of a "high interest type" (H) and with probability 3/4 she is of a "low interest type" (L). After observing her own type, the worker decides whether to obtain a costly education (E) or not (N). The firm observes the worker's education but not her interest. The firm then decides whether to employ the worker as a manager (M) or on a part time contract (C).

The managerial job yields a payoff of 10 to the worker and the part time con- tract job a payoff of 6, irrespective of her type. On the other hand, education

costs the high type 2, whereas it costs the low type 5. The firm's payoff from employing a high type worker as a manager is 10 and from employing her for the contract job is 5. On the other hand, its payoff from employing a low type worker as manager is 0 and from employing her for the contact job is 3.

Find the Perfect BAyseian Equlibrium