Reference no: EM132412210

It's the middle of the spring semester, and you're thinking about applying for a summer internship. You've narrowed your prospects down to two investment banking firms: JP Morgan (JPM) in New York and Legg Mason (LM) in Baltimore. You, as well as everyone else, prefer the JPM internship, but you are hesitant to apply for two reasons. First, there is only one summer intern position at JPM for someone from your school, while there are three at LM. Second, you know that everyone else finds the JPM internship more attractive, and this is likely to make it harder to land a position. Suppose, due to time constraints, you can apply to only one of the internships. Which one should you choose? Suppose 10 students from your school are interested in an investment banking internship at either JPM or LM. Everyone has the same preferences, and each assigns a value of 200 to a JPM internship and a value of 100 to an LM internship. A student's payoff from applying for a JPM internship is 200 only if she is assured of getting it, which is the case only if she is the lone person to apply. The payoff is lower than 200 when more than one apply and generally decreases the more that apply. Analogously, a student's payoff from applying for an LM internship is 100 only if she is assured of getting it, which is the case only if no more than three people apply. (Recall that there are three openings at LM.) When there are more than three applicants, the payoff from applying decreases with an increasing number of applicants.

Suppose a student's beliefs as to what the other 9 students will do as follows: with a probability of 0.2, three of them will apply to JPM and six of them to LM; with a probability of 0.5, four of them will apply to JPM and five of them to LM; and with a probability of 0.3, five of them will apply to JPM and four of them to LM. Assume the student chooses so as to maximize his expected utility, where will he apply?