Coopertition
Coopertition is defined by FIRST as:
Coopertition® produces innovation. At FIRST, Coopertition is displaying unqualified kindness and respect in the face of fierce competition. Coopertition is founded on the concept and a philosophy that teams can and should help and cooperate with each other even as they compete.
At it's heart, coopertition is the idea of fighting hard during matches to win, but outside of matches, doing everything in your power to help other teams succeed.