College Assignment Problems Under Constrained Choice, Private Preferences, and Risk Aversion

Many countries use a centralized admission system for admitting students to universities. Typically, each student reports a ranking of his preferred colleges to a planner, and the planner allocates students to colleges according to the rules of a predefined mechanism. A recurrent feature in these admission systems is that students are constrained in the number of colleges that they can rank. In addition, students normally have private preferences over colleges and are risk-averse. Hence, they face a strategic decision under uncertainty to determine their optimal reports to the planner. We characterize students’ equilibrium behavior when the planner uses a Serial Dictatorship (SD) mechanism by solving an endogenous decision problem. We show that if students are sufficiently risk-averse, their optimal strategy is to truthfully report the “portfolio of colleges” with the highest probabilities of being available. We then analyze the welfare implications of constraining student choice by stressing the differences between the so-called consideration and conditional-allocation effects.