Unknown Rival/Playing With

Basic Trope: A character thinks of another character as his rival, but the other one doesn't notice.

Straight: Alex is constantly trying to prove he's better than Bob and challenging him to battles, while Bob doesn't really notice that Alex considers him a rival.
Exaggerated: Bob doesn't even remember Alex's name after Alex has been constantly hounding him and challenging him to all sorts of contests for years.
Justified: Bob doesn't bother with Alex's rivalry because he has much bigger problems to deal with.
- Alex is five years old, so Bob doesn't take his attempts to be his rival seriously
- Bob is extremely famous fighter, Alex is just one out of countless self-proclaim rivals to him.
Subverted: Once Alex proves himself, Bob acknowledges him as a rival.
- Alternately, the rivalry is in fact mutual, but Alex is Hot-Blooded and constantly yells about said rivalry, while Bob is The Stoic and The Quiet One.
- Another possibility is that the rivalry is mutual, but refusing to acknowledge it is Bob's way of messing with Alex.
Double Subverted: Now that Alex has proven himself he no longer considers Bob to be a rival.
- Alternatively, Bob pretends that the rivalry is a mutual rivalry to make Alex feel better.
- It look like Bob finally consider Alex as his rival, but soon turn out that he misremember him for someone else.
Deconstructed: Alex's constant efforts to make Bob acknowledge him as a rival are the result of an unhealthy obsession with Bob that is slowly destroying his life.
- Alternatively: Bob doesn't see Alex as a threat, and thus underestimates and ignores him. Alex, who has been obsessed with defeating Bob, has spent some time learning Bob's fighting style and his weaknesses, and kicks his ass as a result.
Reconstructed:?
Zig Zagged: Bob can't decide whether or not to take Alex's claims of rivalry seriously
Averted: Alex and Bob are mutual rivals.
Lampshaded: "It's like Bob doesn't even know I'm his rival or something!"
Discussed:

Alex:' "Bob, now I shall put the end to our rivalry!"
Bob:' "...Who the hell are you?"

Played For Laughs: Alex engages in a Zany Scheme in an effort to force Bob to acknowledge him.
Played For Drama: Alex becomes more and more vicious, angry, and ruthless as Bob continues to ignore him, until he reaches the point where, mad with envy and out for blood, he's a very real threat, whether Bob knows it or not.