Check the etymology of "compete" in the Oxford English Dictionary. It tells you that the word derives from Latin, in which "com-" means "together" and "petĕre" has a variety of meanings, which include "to fall upon, assail, aim at, make for, try to reach, strive after, sue for, solicit, ask, seek." Based on this derivation, valid meanings of competition would be "to aim at together," "to try to reach together" and "to strive after together."
Competition can come in many forms. The kind of market competition that economists typically invoke is not about wolves competing in a pen full of sheep, nor is it competition between weeds to choke the flowerbed. The market-based competition envisioned in economics is disciplined by rules and reputations, and those who break the rules through fraud or theft or manipulation are clearly viewed as outside the shared process of competition. Market-based competition is closer in spirit to the interaction between Olympic figure-skaters, in which pressure from other competitors and from outside judges pushes individuals to strive for doing the old and familiar better, along with seeking out new innovations. Sure, the figure-skaters are trying their hardest to win. But in a broader sense, their process of training and coming together under agreed-upon rules is a deeply cooperative and shared enterprise.