one-upmanship

noun2

1. •
   The art or practice of successively outdoing a competitor.

   • They are focused on one-upmanship, which is the essence of a competitive spirit.
2. •
   A succession of instances of outdoing a competitor.

   • Even these debates rarely constituted an exchange of ideas; they more resembled a contest of sectional champions, or a game of righteous, intellectual, and regional one-upsmanship. — 2002