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, 2). 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 0 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. Problem 3 This problem is very similar to the previous one, but has some subtle differences. Consider a game in which, first, nature draws a worker's type from the uniform distribution on [0, 1]. Once the worker observes her type she can choose whether to submit to a test that reveals her ability perfectly. This test costs k E (0, 2). The cost for taking the test is borne by the worker. So a worker's payoff, given a wage w, is just w if she does not take the test. However, if she does take the test, it is w-k. Assume that a worker takes the test when indifferent between taking it and not taking it. The payoff of a firm from hiring a worker of type 0 is the output produced by the worker () minus the wage paid to the worker. Suppose there are two such firms who, after observing whether the worker has taken the test and its outcome if she has, 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. Assume that the two firms, having observed the same data (whether the worker has taken the test, and the rest of the test), hold the same beliefs