Summary: This paper solves for an algorithm that can be used to construct an equilibrium, and under certain conditions, the algorithm terminates in a finite number of steps and can solve for every equilibrium. An equilibrium under incomplete information will typically be inefficient relative to one under complete information. Colleges may not reach full enrollment and may enroll lower quality students; students may apply to too many colleges and may be matched at lower quality colleges. We are interested in studying the value of being a more informed student and find inconclusive results in the interim and ex post because of how students evaluate uncertain outcomes. But ex ante, more informed students are better off, which suggests an incentive for students to learn and be more informed prior to applying to colleges.