Your question is interesting way to look at the "The Gift of the Magi" by O. Henry. If there is a conflict in this brilliant short story, then it is a conflict of outdoing one another in love. Let me give you a bit of the plot to show you this point.
The story open up with these words, "One dollar and eight-seven cents." This point is to show the poverty of this young couple. James and Della. The time is Christmas and they want to give each other something very special, but there is one problem; they are poor. However, both James and Della each have one precious possession of some value. Della has her long hair and James has a pocket watch. They both sell their most prized possession to give each other a present to show their love. Della sells her hair to give James a chain for his watch, and James sells his watch to give a pair of combs for her beautiful hair.
The irony is easy to spot a mile a way. Della cannot use her combs and James cannot use the chain. However, there is something better. There is love. Each out did the other in love. If there is a conflict, it is a a conflict to see who could love more. Both win. Both are wise. No wonder the short story ends with these words: "O all who give and receive gifts, such as they are wisest. Everywhere they are wisest. They are the magi."