rivalry
An ongoing competition between people or groups trying to win.
A rivalry is an ongoing competition between two people, teams, or groups who keep trying to outdo each other. Think of it like a friendly (or not-so-friendly) contest that lasts over time, with each side pushing harder because the other one exists.
Sports teams often develop famous rivalries. The Red Sox and Yankees have competed for over a century, and each game between them carries extra energy because of their history. When there's a rivalry, both sides care more about beating each other than they might care about beating anyone else.
Rivalries aren't just in sports. Two students might develop a rivalry over who gets the highest math scores, pushing each other to study harder. Businesses can be rivals competing for customers. Countries can be rivals competing for power or influence. Siblings sometimes have rivalries over parental attention or family standing.
A rival is the other person or group in the rivalry. Interestingly, having a good rival can actually make you better. When you know someone else is working just as hard, it motivates you to improve. The best rivalries bring out greater effort and achievement on both sides.