Real Dictionary

one-upmanship
uncountable noun: If you refer to someone's behaviour as one-upmanship, you disapprove of them trying to make other people feel inferior in order to make themselves appear more important.

one-upmanship in British English
the practice of, or skill in, seizing an advantage or gaining superiority over others
noun: the art or practice of achieving or maintaining an advantage over others, often by slightly unscrupulous means
noun: the art or practice of achieving, demonstrating, or assuming superiority in one's rivalry with a friend or opponent by obtaining privilege, status, status symbols, etc