Always keeping ahead of others; trying to keep an advantage. (The word one-upmanship was made up by a British humorist, Stephen Potter, on the pattern of such words as sportsmanship and workmanship.)
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.