Why are there no serious rivals to eBay?

Rivals in what line of business? I think there are all sorts of rivals to eBay. But it depends on who you're talking about. As John Stark points out, Amazon is doing very well as a platform for all sorts of retailers to sell all sorts of stuff. Once eBay had the "virtual flea market" space sewn up, that was the obvious next line of expansion for them, and they've been trying for years. But Amazon has a stronger brand, and better customer and vendor relationships. Another area that eBay could have done well in was craft-ish stuff. It's a perfect lots-of-buyers to lots-of-sellers match for their platform. But Etsy is rocking that. They also aren't very good as a "get rid of your extra stuff" tool. Those stores that would put your stuff on eBay for you have mostly vanished. I know a number of people who tried selling extra stuff on eBay an just felt burned. I think Craigslist is doing better here, as old as it is. And if you look at the tech press, you'll see that there are many little companies nipping at eBay's heels. Plenty of people are attempting to eat eBay's lunch. It's a hard problem, as eBay is a classic network-effect business. And after years of complacency, eBay's taking the competition seriously, which makes disruption harder.

No serious rivals because most people who try to rival eBay use basically the same format. The trick to rivalling eBay is to use a format that has significant advantages. This is not impossible but difficult for most people especially those computer nerds who know how to make fancy software but have difficulty establishing relationships.The future of the online auction industry will require more relationship skills than was required in eBay's early days. Personally, I think starting a successful auction site is a lot easier than most people realise.

John Stark has a good answer, but I think that there's a chicken & egg problem too. In order for people to use an auction house, there needs to be people who know about the auction house and will bid on items placed there. If there aren't enough people bidding then the demand for the item will be small and the item won't sell for as much money. Then the seller doesn't really feel like selling at this new auction house anymore. However, if there aren't many sellers, then potential buyers won't visit the site since what they are looking for is not being offered.