This paper studies how rewards based on class rank affect student effort and performance using a game-theoretic classroom competition model and data from the resettlement of Southeast Asian refugees in the US. The paper finds that variation in the presence of strong or weak students changes the incentives and test scores of incumbent students depending on their ability group in accord with the competition model, with increases in the number of strong students lowering effort among strong and weak incumbents but raising the test scores of weak incumbents. The results suggest that competition induced by rank-based rewards within homogeneous ability groups lowers overall effort levels, while the presence of strong students directly augments the performance, but not the effort levels, of weak students despite the competition. The paper also rules out a number of alternative explanations for these school composition effects, including disruptions, teacher-initiated changes in curriculum in response to changing class composition, selective incumbent-student school exit, and endogenous responses of refugee location choices to school performance. [This report was funded by the China National Natural Science Foundation.]