The word "out-jockeys" implies a sense of competition or one-upmanship. Some antonyms that would oppose this notion could be "cooperate," "collaborate," "teamwork," or "support." By using these antonyms, the focus would shift from individuals trying to outdo each other to a group working towards a common goal. Other antonyms that could be used include "noncompetitive," "amicable," or "gracious." These words emphasize a sense of fairness and respect towards others, which is the opposite of the cutthroat nature implied by "out-jockeys." Ultimately, using antonyms like these can help create a more positive, cooperative, and inclusive environment.