A character in a story becomes romantically interested in someone and believes that the best way to get their attention is by being just as good as they are, if not better, at something that they do. The fields can be academic, athletic, or something more mundane like board game tourneys, as long as they can contend. The characters may be strangers to each other, or they may already be familiar with each other; either way, one person develops feelings for and decides to pursue the other. Neither person has to know about the other's harbored affections, or lack thereof, but the suitor must strongly feel that they have something to prove in order to be taken seriously. Said suitor may start out as an Unknown Rival in the beginning, but since success depends on the individual's level of ambition, this is likely to be a plight characteristic of a determined, yet disciplined romantic. It can also happen in the reverse order, i.e 2 characters being straight rivals at first, then one of them coming to like the other's company and care about them. (Friendly Rivalry often also works like this, albeit platonically.) I Was Just Passing Through and The Only One Allowed to Defeat You may come from this.
The courter may actually enjoy the activity they're engaged in, going on to do great things with the prospective relationship giving them just one more reason to perform well. Or, alternatively, the courter may not really care for the activity (at least not initially) and drop it once the courtship ends, since the point of taking it up in the first place had always been to make a good impression on and successfully romance the other party, with whatever other achievements being corollary.
The type of significance one character will have to another will depend on the nature of their rivalry. At best, the object of affection will be left with the impression that they're into the same things and see the suitor as someone (s)he can banter and have fun with. Or, acknowledge the other party as a Worthy Opponent who will provide a challenge, as "iron sharpens iron". At worst, the Love Interest will hate the other person's guts (maybe because of bad sportsmanship from one side or the other), but that suitor will still prefer the negative attention to that love interest not even knowing they exist.
Compare Friendly Rivalry or Defeat Means Friendship for non-romantic examples, although they could evolve into this trope. Contrast Foe Romantic Subtext and Dating Catwoman for when the two are outright enemies.
- A 2016 commercial for an upgraded Fitbit fitness tracker bracelet has a man watching a woman jog by. He tries to keep up with her but she outpaces him. After a montage of him working out, he tries again and does well enough to gain her notice... before she hits the next leg of her route: a flight of stairs built up a tall hill. Then he is left behind once again. The ad was soon removed because although it was intended to look romantic, the alternate interpretation was that the guy was a bit of a creep for pursuing his interest this way.
- Ayakashi Triangle: Soga is almost obsessed with being Matsuri's rival, but after the latter is turned female, Soga can't help but fall for him. Both feelings are one-sided; Matsuri admires Soga as a senior colleague rather than a rival, even if he'll call him his rival, and doesn't notice Soga's infatuation.
- Aoi and Sakura's romance in Love Gene XX grows out of their rivalry (mostly one-sided, as Aoi is the only one obsessed with it) over the position of the top student of the Kingdom Academy.
- Deconstructed in Cupid's Chocolate-ing. Xueli's mother convinces her that a good way to get the attention of her childhood friend Haoyi is to compete and be better than him at their studies. Xueli becomes so obsessed with their rivalry that Haoyi ends up purposely dropping his grades and distances from her, which seems to have been the real intention of Xueli's mother all along.
- In Kaguya-sama: Love is War, the protagonists want to date each other but don't have the balls to confess, so they devise an elaborate social game based on goading/seducing the other into making the first move. After a good deal of Character Development, Kaguya is able to admit that the game doesn't matter anymore, because she knows that Shirogane would absolutely reciprocate any confession she made (though not in a pathetic, desperate way, like she fantasized about at the start) and that neither of them need to prove anything to each other. In the end it's All for Nothing anyway; Shirogane confesses first, but Kaguya responds with a intensely physical French kiss, which embarrasses her even more than confessing would have. Luckily, by this point, she's able to have a sense of humor about the whole thing.
- Teasing Master Takagi-san has an unconscious example. Takagi knows that her friendship with Nishikata is really a Long Game to make him pay attention to her; Nishikata doesn't. Presumably she'll confess the truth once they're out of middle school.
- In Night World, Jez Redfern and Morgead Blackthorn were friends as children, then became rivals over dominance of their gang as teenagers. Morgead secretly admired and loved Jez, but didn't know how to express himself, while Jez thought he genuinely hated her. They eventually sort out their real feelings and mutually fall in love.
- Jake Peralta and Amy Santiago in Brooklyn Nine-Nine. Team Dad Captain Holt says this at their wedding:
Holt: [It] has been a true pleasure to watch your distracting childish rivalry evolve into a distracting childish courtship and now into what I'm sure will be a distracting childish marriage.
- Mindy Crenshaw from Drake & Josh is introduced in the first season as a classmate who outdoes Josh, (specifically in the sciences), believes herself to be smarter than him, and insults his intelligence every chance she gets. It's not until the season 3 episode "Mindy's Back" after Josh gets fed up and confronts her that Mindy confesses that all her arrogance was a front to hide her admiration for him. From that point on, they end up in an on-and-off relationship until the Series Finale.
- Never Have I Ever: This is of the "crush stems from rivalry" variety between Devi and Ben. They kiss in the first season's finale.
- The Relationship Values in Dragon Age II are placed on the Friendship-Rivalry scale, depending on whether the respective party member sees Hawke as a confidante to trust or as a contrarian to prove wrong. Initiating and completing a Romance Sidequest with any of the four Love Interests is possible regardless of whether you are friends or rivals with them (only the overall intensity of the relationship counts), and romancing a rival is very much a Slap-Slap-Kiss deal.
- In Hades, Zagreus and Thanatos begin to realize their feelings for each other in a series of Body Count Competitions while Thanatos assists in Zagreus's escapes. When Zagreus starts regularly winning these competitions and proves he doesn't really need the help, Thanatos is forced to confront the underlying reason for why he's defying Hades and risking his station for Zagreus: he just wants to be with him.
- The Adventures of Jimmy Neutron: Boy Genius has both Cindy Vortex and Jimmy himself, who both even have their own respective crushes (Nick Dean and Timmy Turner for Cindy, Betty Quinlan and "Win, Lose and Kaboom's" April for Jimmy) while maintaining their own academic rivalry, competing for the reputation of "smartest kid in school". Over the course of the show, however, their relationship develops and goes on to encompass instances of mutual jealousy, an aphrodisiac ("Love Potion 976/J"), and a future timeline where they are expressly married.