Perfect Bayesian Equilibrium

Problem 2 Consider a game in which, first, nature draws a worker's type from the uniform distribu- tion on [0, 1]. Once the worker observes her type she can choose whether to acquire a certificate. This certificate costs k e (0, }). The cost of being certified is borne by the worker. A worker's pay- off, given a wage w, is just Ow if she does not get certified. However, if she does get certified, it is Ow - k. Assume that a worker gets certified when indifferent. The payoff of a firm from hiring a worker of type O is the output produced by the worker (0) minus the wage paid to the worker. Suppose there are two such firms who, after observing whether the worker has been certified, bid for her services. (a) What are the strategies and beliefs for the firms? (b) What is a strategy for a worker? (c) Find a PBE of this game. As a simplification, you can impose the restriction that the two firms, having observed the same data (whether the worker has been certified), hold the same beliefs