| Much of the matching literature assumes that players know their own preferences prior to entering into a matching process, but this assumption typically does not hold. This paper will consider a sequential college admissions game where students apply to colleges, colleges admit students, and students decide where to enroll (conditional on admission offers). The utility from a match is based on a student's and college's qualities, and those utilities induce a preference ordering over matching partners. The incomplete information will come from how students may not know a college's true quality, only its distribution; with heterogeneity in the students' incomplete information, students will rank the colleges differently as well as inaccurately. This asymmetry in the students' private information will lead to uncertain outcomes, and the equilibrium concept we will use is that of a perfect Bayesian equilibrium.;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. |
