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]WordNet (r) 3.0 (2006):
one-upmanship n 1: the practice of keeping one jump ahead of a friend or competitor