3. (20 points) Consider the following signalling game. e First, nature draws the productivity of a worker, which is 4 with probability % and 2 with probability 1 3- o The worker then decides whether or not to get educated. Let E denote education and N denote no education and assume that education costs 1 for the type with productivity 4 and 3 for the type with productivity 2. e A firm then observes whether or not the worker is educated. Due to some (job killing!) regulations the firm must pay a wage of w with 2 0 if the firm hires a high productivity worker and 2 w