This paper studies the effects of incentive mechanisms and of the competitive environment on the interaction between schools and students, in a set-up where the students' educational attainment depends on their peer group, on their effort, and on the quality of the school's teaching. We show that increasing the power of the incentive scheme and the effectiveness of competition may have the counterintuitive effect of lowering the students' effort, with ambiguous effects on their attainment. In a simple dynamic set-up, where the reputation of the schools affects recruitment, we show that increased competition leads to segregation of pupils by ability.