The College Signaling Game Nature Low Moderate High Applicant College College No No College No college college college Employer Manager Clerk Manager Clerk Manager Clerk Manager Clerk Manager Clerk Manager Clerk Applicant 9 4 15 10 11 15 10 13 8 15 10 Employer 4 7 4 7 7 6 7 14 7 14 7
We’ll now show how a college degree can get you a better job even if it
doesn’t make you a better worker. Consider a two-player game between a
prospective employee, whom we’ll refer to as the applicant, and an employer. The applicant’s type is her intellect, which may be low, moderate,
or high, with probability 1/3 , 1/2 , and 1/6 , respectively. After the applicant
learns her type, she decides whether or not to go to college. The personal
cost in gaining a college degree is higher when the applicant is less intelligent, because a less smart student has to work harder if she is to graduate. Assume that the cost of gaining a college degree is 2, 4, and 6 for an applicant who is of high, moderate, and low intelligence, respectively.
The employer decides whether to offer the applicant a job as a manager
or as a clerk. The applicant’s payoff to being hired as a manager is 15,
while the payoff to being a clerk is 10. These payoffs are independent of
the applicant’s type. The employer’s payoff from hiring someone as a
clerk is 7 (and is the same regardless of intelligence and whether or not
the person has a college degree). If the applicant is hired as a manager,
then the employer’s payoff increases with the applicant’s intellect, from
4, to 6, to 14, depending on whether the applicant has low, moderate, or
high intellect, respectively. Note that the employer’s payoff does not
depend on whether or not the applicant has a college degree. The extensive form of this game is shown in the accompanying figure. Find a
PBNE in which students of low intellect do not go to college and those of
moderate and high intellect do.
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