Definition: A character that actively competes against the protagonist.
What You Need To Know: Rivals are one of the corner stones of Anime and manga. They are usually introduced as a protagonist’s long time acquaintance or first enemy, and initially have an advantage over the protagonist. Rivals walk the fine line between comrade and foe throughout most stories, and end up helping the protagonist become a stronger person.
Because most protagonists are very personable, Rivals tend to be the opposite. If the protagonist is friendly, then the Rival will be rude. If the protagonist is arrogant, then the Rival will be cool and collected. Writers and artists even go so far as to give the rival and protagonist opposite physical characteristics, such as different heights, hair style, or even color schemes.
Even though Rivals start off as stronger than the protagonist, the nature of the protagonist’s role requires them to be defeated. This sets most Rivals down a destructive spiral. A lot of Rivals tend to have a superiority and inferiority complex. They believe that they are the best, and cannot mentally accept otherwise. They may even become obsessed with the protagonist in order to learn why they were defeated.
Rivals are not “arch-enemies.” A lot of Rivals end up working alongside the protagonist and his/her crew, adopting an almost Tsundere personality. They like having someone to compete with, even if they can’t admit it themselves. The Rival’s journey is to become less individualistic and more trusting.
Still, at the end of the day, a lot of Rivals are kinda jerks.
My Western Take: In fiction, you gauge the value of a hero by the obstacles they need to overcome. In a lot of stories, these obstacles are personified as an antagonist. The most successful antagonists are often just inverted version of the protagonist. Batman and The Joker, Luke Skywaker and Darth Vader, Cal and Stanford. Admittedly, western fiction doesn’t play around with the concept as much as I’d like. In manga and anime, Rivals are less negative versions of traditional antagonists. They want to defeat the protagonist, but generally don’t wish any real ill will towards them or their friends. They are equivalent to the western term, “Frienemies.”