In her book Widening the Circle: The Power of Inclusive Classrooms, Mara Sapon-Shevin summarizes the case against competition nicely:
Low achievers are rarely motivated by competition because they do not perceive themselves as having a chance to win. A small number of high achievers may be motivated, but they are generally motivated to "win" rather than to learn. Competition often encourages cheating, poor interpersonal behavior, and sometimes even lower achievement (if there's a prize to the first child who finishes a book, I am unlikely to undertake reading the long and challenging book that might actually stretch me). And for all students, competition damages community and student's willingness to help one another succeed.For more on competition:
Treating Kids like Pets
Competition is for the strong. Public education is for everyone. See the problem?
No Grades and Group Work