signaling and bayesian nash?

[chem]

. A worker can have either high or low ability, each with probability ½. A worker knows his ability, but a firm which wants to hire the worker does not. The worker, whether a high or low ability type, can choose between additional education or not. Choosing additional education does not enlarge the worker’s productivity but may serve as a signal to the firm: a high ability worker can choose education without additional costs, whereas for a low ability worker, the cost of education is e > 0. The firm chooses either a high or a low wage, having observed whether the worker took additional education or not. The payoff to the firm is equal to the productivity of the worker minus the wage. The payoff to the worker is equal to the wage minus the cost of education. If, however, the worker’s payoff is lower than the worker’s reservation utility, he chooses not to work at all and to receive his reservation utility, leaving the firm with 0 payoff. Denote the productivity of the high and low ability worker by pH and pL, respectively, and denote the high and low wages by wh and wl. Finally, let rH and rL denote the reservation utilities of both worker types. Let pH = 10, pL = 8, wh = 6, wl = 4, rH = 3, rL = 2, and e = 3.
a) Determine the extensive form of this game. Give also the corresponding normal form.
b)Analyse this game as a signaling game and find the perfect Bayesian equilibria.