one-up‧man‧ship /wʌnˈʌpmənʃɪp/ noun [uncountable]
attempts to make yourself seem better than other people, no matter what they do

[TahlilGaran] Dictionary of Contemporary English ▲

one-upmanship
if something someone does is one-upmanship, they are trying to make other people admire them by doing it in a better or more clever way than someone else.
There is a great deal of one-upmanship among children anxious to wear the most fashionable clothes.

[TahlilGaran] English Idioms Dictionary ▲

one-upmanship
the ability to keep ahead of others, the ability to keep an advantage
His one-upmanship and his desire to always be better than everyone else makes many people tired of him.

[TahlilGaran] English Idioms Dictionary ▲

one upmanship
v., informal Always keeping ahead of others; trying to keep an advantage.
No matter what I do, I find that Jim has already done it better. He's an expert at one-upmanship.
Jack took the news to the principal while we were still talking about it. He's very quick to practice one-upmanship.
Compare: ONE UP. (The word one-upmanship was made up by a British humorist, Stephen Potter, on the pattern of such words as sportsmanship and workmanship.)

[TahlilGaran] English Idioms Dictionary ▲