Schools should because if they do more kids will be interested in learning and joining. They will also get more people to do things if the make up fun ways to learn instead of the boring lectures and group work that teacher think is fun but its totally not. Yes they should.
There is an obvious link between becoming better at something and competition. When there is competition in school, there will be a greater want to succeed. Students will strive to succeed instead of blowing off "Boring ol' school" Impliment game theory and watch the grade skyrocket. This needs to be implimented now.