Take cues from existing paradigms:
A successful competitor to eBay would have completely disrupt eBay's current business model -- ie the level of disruption Craigslist has caused for the classifieds industry. That probably means some sort of free service - perhaps with only specialist categories requiring a listing fee/cut of final sale (in the same way CL only charges for jobs and a handful of other categories).
A successful competitor to eBay would have to have a very clever strategy to overcome the network effect eBay has. Look at how Zuckerberg launched Facebook in the face of MySpace and Friendster's network effect. He concentrated on a niche (just Harvard, than just students), owned it and then enlarged. I would therefore specialize in a niche area and then once you have pwned eBay in that area, expand out.
