This paper introduces a novel framework for modeling diversity using the theory of majorization and applies it to school choice problems. We consider a school with limited capacity that must select students from an applicant pool, where each student is classified into types (e.g., by race, gender, or socioeconomic status). Within this setting, we ask: How should we compare the diversity of student groups? And what admissions procedure balance the school's goal of admitting students with the highest priority (e.g., academic merit, proximity to the school) and achieving a diverse student body?

An agent engages in sequential search. He does not directly observe the quality of the goods he samples, but he can purchase signals designed by profit maximizing principal(s). We formulate the principal-agent relationship as a repeated contracting problem within a stopping game, and characterize the set of equilibrium payoffs. We show that when the agent's search cost falls below a given threshold, competition does not impact how much surplus is generated in equilibrium nor how the surplus is divided. In contrast, competition benefits the agent at the expense of total surplus when the search cost exceeds that threshold. Our results challenge the view that monopoly decreases market efficiency, and moreover, suggest that it leads to more information provision than does competition.