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Becca and Danielle are two of the best students in their prep school and are applying to colleges this year. Since many colleges only accept a limited number of students from a particular high school, the probability that Becca is accepted by a college decreases if Danielle also applies to it (and vice versa). Suppose Becca and Danielle must choose between applying to either 5 or 10 colleges. The following payout matrix shows the probabilities that Becca and Danielle will be accepted by their “first choices” under different combinations of strategies of the two high school seniors. The top right entry in each cell is the probability that Becca will be accepted by her first choice and the bottom left entry is the probability that Danielle will be accepted by her first choice.
Now, let’s change the game. Suppose Becca is the daughter of a very wealthy woman who has donated millions of dollars to her prep school. The school’s headmaster recently offered Becca’s mom the following deal. “If Becca only applies to 5 colleges,” the headmaster told her, “I will personally call my contacts at the colleges and chat with them about Becca.” Looking uncomfortable, he said, “But if Becca applies to more than 5 colleges, I won’t call any of them.” Becca’s mom exploded, angry that he wasn’t offering to make calls to 10 colleges. He replied, “It’s not that I’m lazy; It’s that I want my calls on behalf of Becca to benefit other students as well. I think it is only fair.”
The National Longitudinal Survey of Freshmen • Sample of 4160 college students at 28 highly selected colleges who were freshman in the fall of 1999. • Surveyed over 4 years of college
