In this thread on why trophies are often cup-shaped /u/TheJucheisLoose explains that vessels filled with olive oil were awarded at ancient Greek and Roman events. Other theories on trophies and specifically cup-shaped trophies are also discussed, but that's the most ancient tradition mentioned.

http://www.reddit.com/r/AskHistorians/comments/1nrnji/why_are_trophies_often_cups/