one-upmanship

from WordNet (r) 3.0 (2006)

one-upmanship
    n 1: the practice of keeping one jump ahead of a friend or
         competitor

from The Collaborative International Dictionary of English v.0.48

one-upmanship \one-upmanship\ n.
   The attitude or practice of trying to keep one step ahead of
   a friend or competitor; vigorous competitiveness.
   [WordNet 1.5 +PJC]