I have always considered college fraternities to be a nuisance. They appear to be mostly about drinking and making a mess on campus, although they also organize some activities for the public good. As any social club, there may also be some value of being a member beyond the socializing.
Sergey Popov and Dan Bernhardt build a model of two-sided selection of fraternities and its members. Candidates may differ by ability, and membership in a fraternity may be viewed as a signal of ability by employers. The paper shows that anything can happen in terms of equilibrium: informative, uninformative, good students, bad students or no students in fraternities. But using data about student grades at the University of Illinois, Popov and Bernhardt show that the following equilibrium is most likely: The best students shy away from fraternities while the worst ones do not get in. Fraternities only have students with medium abilities. But would these students have better grades if they did not spend significant time in fraternity activities?