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3. [15 points] Should you pursue a master’s degree after graduating from college? And what would be the socio-economic 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 course you know your own ability, but a potential employer (Player 2) does not. However, it is common knowledge that half of the college graduates are type H and half of them are type L. In this model, earning a master’s degree does not change your type (i.e. your ability) but it may still help to improve your employment prospects.
A master’s degree will cost you $30K if you are of type H, and $60K if you are of type L Regardless of your type, you earn $80K if Player 2 employs you and $0 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 seeking a job from Player 2, you must decide whether to get a master’s degree (i.e. play G – short for graduate education) or not (i.e. play B – short for bachelor’s).
Player 2 must decide whether to employ you (i.e. play E) or not (i.e. 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 profit of $70K (net of the salary she pays you); but if you turn out to be type L, Player 2 makes a profit of –$80K (i.e. a net loss). If Player 2 does not employ you, her profit is $0.
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 final outcome.

(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 fill in the blanks if applicable.)
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 always plays G, i.e. every graduate with low ability gets a master’s degree but a graduate with high ability may or may not do so? (Circle the right answer and fill in the blanks if applicable.)
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 profitable.
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 – when graduate education incurs costs without improving productivity.
Explain your answers to (d) briefly on the next page.

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