4. [12 points] Should you pursue a master's degree aer graduating from college? And what would be the socioeconornic consequences of your decision? Here is one way to analyze the problem, using game theory. You (Player 1) may have high ability (H) or low ability (L) of coluse you know your own ability, but a potential employer (Player 2) does not However, it is common knowledge that 20% of college graduates are type H and 80% of them are type L In this model, earning a master's degree does not change your type (ie your ability) but it may still help to improve your employment prospects. A master's degee will cost you $20K if you are of type H, and $40K if you are of type L Regardless of your type, you earn $60K if Player 2 employs you and 30 if she does not. In either case, from your earnings you must pay back the cost of your master's degree if you have gotten one. Before seeldng a job from Player 2, you must decide whethrn' to get a master's degree (irei play G 7 short for graduate education) or not (i.ei play B 7 short for bachelor's) Player 2 must decide whether to employ you (i.e. play E) or not (Le, play N) At the time of her decision, she can see if you have a master's degree and she can base her decision upon that fact; but she cannot directly observe your type, or the cost you have incurred for your master's degree if you have one. If she employs you and you turn out to be type H, Player 2 makes a prot of S90K (net of the salary she pays you); but if you turn out to be type L, Player 2 makes a prot of 7360K (ie a net loss). If Player 2 does not employ you, her prot is 30. Both players are wise to all aspects of this game, and they will make inferences and decisions based on what he or she knows to be the strategy of the other. (a) Model this situation as a Game in Extensive Form with Imperfect Information Draw the game tree and the Information sets. Specify the player at each information set and the payoffs at each nal outcome. (Question 4 continues on the next page) Page 8 of 12 4. (continued) (b) Is there an equilibrium in which Player 1 always plays B regardless of his type, i.e. nobody gets a master's degree? (Circle the right answer and ll in the blanks ifapplicqble.) Yes; and in this equilibrium, Player 2 plays E with probability if Player 1 has a master's degree; Player 2 plays E with probability if Player 1 only has a bachelor's; If Player 1 is of type H, he gets employed with probability ; If Player 1 is of type L, he gets employed with probability /No, there is no such equilibrium. (c) Is there an equilibrium in which a Player 1 of type L almys plays G, ie every graduate with low ability gets a master's degree but a yaduate with high ability may or may not do so? (Circle the right answer and/ill in the blanks i/applicablei) Yes; and in this equilibrium, Player 2 plays E with probability if Player 1 has a master's degree; Player 2 plays E with probability if Player 1 only has a bachelor's; If Player 1 is of type H, he plays G with probability No, there is no such equilibrium. (d) Consider an equilibrium in which a Player 1 of type H always plays G. In this equilibrium, Player 2 plays E with probability if Player 1 has a master's degree; Player 2 plays E with probability if Player 1 only has a bachelor's; If Player 1 has a master's degree, then the probability that he is of type H is If Player 1 is of type L, he plays G with probability According to this model and this equilibrium, Amongst college graduates with high abilities, percent are unemployed, even when employing them would be socially protable. Amongst college graduates with low abilities, percent are employed, even when employing them incurs social loss. Amongst all college graduates percent go on to get master's degrees, even when it is socially wasteful 7 when graduate education incurs costs without improving productivity. Explain your answers to (d) briey on the next page Page 9 of 12